Why Word Problems Are Harder Than Arithmetic
A child who can compute $48 \times 7 = 336$ in three seconds can still freeze on "Maya has 7 boxes with 48 cookies each — how many cookies total?" The math is identical. The barrier isn't arithmetic — it's translation: turning English into a math sentence.
Three translation skills underlie every word problem:
Reading for the question — what is actually being asked?
Identifying the operation — which arithmetic operation does the situation describe?
Building the equation — converting the words into numbers and symbols.
Most children master step 1 quickly. Step 2 takes longer (and is what keyword-hunting strategies like CUBES try to teach). Step 3 — equation-building — is where most word-problem struggles live, and it's the focus of the 5-step method below.
How to Solve Any Math Word Problem — The UPSCC Method
A 5-step framework that works for word problems from Grade 1 through Grade 12:
U — Understand the problem.
P — Plan the approach.
S — Solve with the plan.
C — Check the answer makes sense.
C — Communicate the answer with units.
Step 1 — Understand (Read it Twice)
Read the problem twice. First pass: get the story. Second pass: identify what you need to find. Underline the question. Circle the numbers. Box the units (kg, $, hours).
Step 2 — Plan (Pick the Operation)
Ask three questions:
"Is the total getting bigger or smaller?" → bigger → add or multiply; smaller → subtract or divide.
"Are the items the same or different?" → same repeated → multiplication/division; different combined → addition/subtraction.
"Is there a 'per' or 'each' in the problem?" → probably multiplication or division.
If the operation still isn't clear, sketch the situation. A bar diagram or set diagram makes the structure visible.
Step 3 — Solve
Write the equation. Compute. Show working — every step on its own line. No silent steps.
Step 4 — Check
Substitute the answer back into the original story. Does it fit? Is it the right size — about what you'd expect?
Step 5 — Communicate
Write the answer in a sentence with units. "Maya has 336 cookies." Not just "336."
The 5-Step Method in Action — One Worked Example
Problem. A baker uses 3 cups of flour for one cake. How many cups does she need for 14 cakes?
U — Understand. She bakes 14 cakes. Each cake uses 3 cups. Find the total flour.
P — Plan. Same amount per cake × number of cakes = total. So multiply.
S — Solve. $3 \text{ cups} \times 14 \text{ cakes} = 42 \text{ cups}$.
C — Check. Sanity check: 1 cake = 3 cups, 10 cakes ≈ 30 cups, 14 cakes ≈ 42 cups. ✓
C — Communicate. The baker needs 42 cups of flour.
155 Math Word Problems by Topic
Below are 155 word problems sorted into 15 categories. Each problem is labelled with a grade band and includes the answer and brief method. Problems within each category are ordered roughly Easy → Medium → Stretch.
Addition Word Problems (Problems 1–15)
Grade bands: K-3 mostly; Grade 4–5 for the stretch entries.
1. Sam has 4 apples. His sister gives him 3 more. How many apples does Sam have now?
Answer: 4 + 3 = 7 apples.
2. A classroom has 12 boys and 14 girls. How many students are in the classroom?
Answer: 12 + 14 = 26 students.
3. Lily reads 18 pages on Monday and 23 pages on Tuesday. How many pages does she read in total?
Answer: 18 + 23 = 41 pages.
4. A library has 234 fiction books and 187 non-fiction books. How many books does it have in total?
Answer: 234 + 187 = 421 books.
5. On a school trip there are 3 buses. The first bus has 36 students, the second has 41, and the third has 39. How many students went on the trip?
Answer: 36 + 41 + 39 = 116 students.
6. A box contains 24 red balls, 36 blue balls, and 19 green balls. How many balls are in the box?
Answer: 24 + 36 + 19 = 79 balls.
7. Maya saved $45 in January, $62 in February, and $58 in March. How much did she save in three months?
Answer: $45 + $62 + $58 = $165.
8. A cinema sold 124 tickets on Friday, 178 tickets on Saturday, and 145 tickets on Sunday. How many tickets did it sell on the weekend?
Answer: 124 + 178 + 145 = 447 tickets.
9. A farmer has 1,236 hens and 879 ducks. How many birds does he have in total?
Answer: 1,236 + 879 = 2,115 birds.
10. During a charity drive, Class 5A collected $1,205. Class 5B collected $1,478. Class 5C collected $987. How much did the three classes collect together?
Answer: 1,205 + 1,478 + 987 = $3,670.
11. A school has 5 sections in Grade 6, with 32, 35, 31, 34, and 33 students respectively. What is the total number of Grade 6 students?
Answer: 32 + 35 + 31 + 34 + 33 = 165 students.
12. Anna's family drove 215 km on the first day, 248 km on the second day, 196 km on the third day, and 312 km on the fourth day. What was the total distance?
Answer: 215 + 248 + 196 + 312 = 971 km.
13. A factory produced 4,567 toys in week one and 5,824 toys in week two. How many toys did it produce in two weeks?
Answer: 4,567 + 5,824 = 10,391 toys.
14. A fundraiser collected donations of $245, $189, $312, $97, and $403. What was the total donation amount?
Answer: 245 + 189 + 312 + 97 + 403 = $1,246.
15. (Stretch.) A library added 1,236 books in 2024 and 1,478 books in 2025. If the library had 12,890 books before 2024, how many books does it have at the end of 2025?
Answer: Start + 2024 + 2025 = 12,890 + 1,236 + 1,478 = 15,604 books.
Subtraction Word Problems (Problems 16–30)
16. Tom has 12 pencils. He gives 5 to his friend. How many pencils does he have left?
Answer: 12 − 5 = 7 pencils.
17. A bag contains 50 marbles. If 18 are red and the rest are blue, how many are blue?
Answer: 50 − 18 = 32 blue marbles.
18. Mia had $85. She spent $37 on a book. How much money does she have left?
Answer: 85 − 37 = $48.
19. A pizza has 12 slices. If 7 slices are eaten, how many slices remain?
Answer: 12 − 7 = 5 slices.
20. A car travels 420 km on a full tank. If it has travelled 287 km, how much further can it go?
Answer: 420 − 287 = 133 km.
21. A school has 638 students. 245 are in primary school. How many are in middle and high school?
Answer: 638 − 245 = 393 students.
22. A water tank holds 5,000 litres. After watering the garden, 1,847 litres are left. How many litres were used?
Answer: 5,000 − 1,847 = 3,153 litres.
23. A shopkeeper had 1,250 eggs. He sold 875 eggs in one day. How many eggs are left?
Answer: 1,250 − 875 = 375 eggs.
24. Emma was 4 years old in 2018. In what year will she turn 21?
Answer: 21 − 4 = 17 years from 2018 → 2018 + 17 = 2035.
25. A library had 8,432 books. After lending 2,178 to schools, how many books are left in the library?
Answer: 8,432 − 2,178 = 6,254 books.
26. A theatre seats 1,200 people. If 879 tickets have been sold for a show, how many seats are still empty?
Answer: 1,200 − 879 = 321 seats.
27. A farmer's field produces 12,500 kg of wheat. He sells 7,840 kg and donates 1,500 kg. How much wheat is left?
Answer: 12,500 − 7,840 − 1,500 = 3,160 kg.
28. A bakery baked 540 muffins. By noon, 312 had been sold. By 4 pm, another 154 had been sold. How many muffins are left at 4 pm?
Answer: 540 − 312 − 154 = 74 muffins.
29. Aria's account balance is $2,485. She withdraws $578 and pays a $42 bill. What is her balance now?
Answer: 2,485 − 578 − 42 = $1,865.
30. (Stretch.) A factory makes 1,200 toys a week. Of these, 87 are returned as defective and 156 are kept for quality testing. The rest are sold. If the factory sells toys at $12 each, how many dollars does it earn per week?
Answer: Toys sold = 1,200 − 87 − 156 = 957. Earnings = 957 × $12 = $11,484.
Multiplication Word Problems (Problems 31–45)
31. A box contains 6 chocolates. How many chocolates are in 7 such boxes?
Answer: 6 × 7 = 42 chocolates.
32. Each pencil costs $3. Maya buys 9 pencils. How much does she pay?
Answer: 3 × 9 = $27.
33. A classroom has 8 rows of desks with 5 desks in each row. How many desks are there?
Answer: 8 × 5 = 40 desks.
34. A bookshelf has 12 shelves, and each shelf holds 24 books. How many books does the bookshelf hold?
Answer: 12 × 24 = 288 books.
35. A bus carries 45 passengers. A fleet of 18 buses runs each morning. How many passengers do the buses carry in total each morning?
Answer: 45 × 18 = 810 passengers.
36. A theatre has 25 rows with 36 seats per row. How many seats are in the theatre?
Answer: 25 × 36 = 900 seats.
37. A factory produces 145 cars per day. How many cars does it produce in 30 days?
Answer: 145 × 30 = 4,350 cars.
38. Each carton holds 24 bottles. How many bottles are there in 72 cartons?
Answer: 24 × 72 = 1,728 bottles.
39. A rectangle has length 28 cm and width 15 cm. What is its area?
Answer: 28 × 15 = 420 cm².
40. A school orders 36 boxes of pencils. Each box has 144 pencils. How many pencils are ordered in total?
Answer: 36 × 144 = 5,184 pencils.
41. A train travels at 85 km per hour for 6 hours. How far does it travel?
Answer: 85 × 6 = 510 km.
42. A family of 5 visits a restaurant. Each meal costs $18.50. What is the total cost?
Answer: 5 × $18.50 = $92.50.
43. A factory ships 248 boxes per truck. If 15 trucks make one delivery round, how many boxes are shipped in one round?
Answer: 248 × 15 = 3,720 boxes.
44. A baker decorates 12 cupcakes per minute. How many cupcakes does she decorate in 45 minutes?
Answer: 12 × 45 = 540 cupcakes.
45. (Stretch.) A classroom has 7 rows of desks. Each row has 6 desks. Each desk has 4 legs. How many desk legs are in the classroom?
Answer: 7 × 6 × 4 = 168 legs.
Division Word Problems (Problems 46–60)
46. 24 cookies are shared equally among 6 children. How many cookies does each child get?
Answer: 24 ÷ 6 = 4 cookies each.
47. A teacher has 56 stickers to give equally to 8 students. How many stickers does each student get?
Answer: 56 ÷ 8 = 7 stickers each.
48. 144 pencils are packed into boxes of 12. How many boxes are filled?
Answer: 144 ÷ 12 = 12 boxes.
49. A baker makes 96 cupcakes. She arranges them on trays of 8. How many trays does she need?
Answer: 96 ÷ 8 = 12 trays.
50. A school spent $450 to buy 18 footballs. What is the cost of one football?
Answer: 450 ÷ 18 = $25 each.
51. A car travels 360 km on 30 litres of fuel. How many kilometres does it travel per litre?
Answer: 360 ÷ 30 = 12 km per litre.
52. 528 students are divided equally into 22 classrooms. How many students are in each classroom?
Answer: 528 ÷ 22 = 24 students.
53. A 750-page book is read at 25 pages a day. How many days will it take to finish?
Answer: 750 ÷ 25 = 30 days.
54. A roll of ribbon is 480 cm long. It is cut into 16 equal pieces. What is the length of each piece?
Answer: 480 ÷ 16 = 30 cm.
55. A jet covers 2,400 km in 4 hours. What is its average speed in km/h?
Answer: 2,400 ÷ 4 = 600 km/h.
56. 1,260 chocolates are packed into boxes of 36. How many boxes are needed?
Answer: 1,260 ÷ 36 = 35 boxes.
57. A factory packs 9,720 pencils into cartons of 162. How many cartons are filled?
Answer: 9,720 ÷ 162 = 60 cartons.
58. A 6,500 kg load is to be carried by trucks. Each truck carries 250 kg. How many trucks are needed?
Answer: 6,500 ÷ 250 = 26 trucks.
59. A school's annual fee for 365 students is $328,500. What is the annual fee per student?
Answer: 328,500 ÷ 365 = $900 per student.
60. (Stretch — division with remainder.) A baker has 100 cupcakes to arrange into boxes of 8. How many full boxes will she make, and how many cupcakes will be left over?
Answer: 100 ÷ 8 = 12 remainder 4 → 12 full boxes, 4 cupcakes left over.
Mixed Operations Word Problems (Problems 61–70)
These require two or more operations applied in order. Test of multi-step reasoning.
61. Sam buys 3 notebooks at $4 each and 2 pens at $2 each. How much does he spend?
Answer: (3 × 4) + (2 × 2) = 12 + 4 = $16.
62. A school has 24 classrooms with 35 students each. If 168 students are absent today, how many are present?
Answer: (24 × 35) − 168 = 840 − 168 = 672 students present.
63. Mia earns $15 per hour. She works 6 hours on Monday and 8 hours on Tuesday. How much does she earn in total?
Answer: $15 × (6 + 8) = $15 × 14 = $210.
64. A baker has 240 cookies. She sells them in packs of 6 at $4 per pack. How much money does she earn if all packs sell?
Answer: Number of packs = 240 ÷ 6 = 40. Earnings = 40 × $4 = $160.
65. A library borrows 28 books per day for 5 weekdays and 42 books per day on weekends. How many books does it lend in a week (7 days)?
Answer: (28 × 5) + (42 × 2) = 140 + 84 = 224 books.
66. A printer prints 35 pages per minute. How many pages can it print in 1 hour 12 minutes?
Answer: Time = 60 + 12 = 72 minutes. Pages = 35 × 72 = 2,520 pages.
67. A farmer has 245 cows and 178 goats. Each cow gives 12 litres of milk a day and each goat gives 2 litres. How much milk does the farmer get in a day?
Answer: (245 × 12) + (178 × 2) = 2,940 + 356 = 3,296 litres.
68. A school orders 18 boxes of textbooks. Each box has 24 books costing $15 each. What is the total cost?
Answer: 18 × 24 × 15 = $6,480.
69. Maya wants to save $4,800 for a trip. She has already saved $1,250. If she saves $175 per week from now, how many more weeks until she reaches her goal?
Answer: Remaining = 4,800 − 1,250 = $3,550. Weeks = 3,550 ÷ 175 = 20.29, so 21 weeks (round up because partial week's worth doesn't reach the goal).
70. (Stretch.) A taxi charges $3 base fare plus $1.50 per kilometre. Aria takes a taxi for 12 km. Her sister takes the same kind of taxi for 18 km. How much do the two trips cost together?
Answer: Aria: 3 + (1.50 × 12) = 3 + 18 = $21. Sister: 3 + (1.50 × 18) = 3 + 27 = $30. Total = $51.
Fraction Word Problems (Problems 71–82)
71. Maya has $\tfrac{1}{2}$ of a pizza. She eats $\tfrac{1}{4}$ of the pizza. How much pizza is left?
Answer: $\tfrac{1}{2} - \tfrac{1}{4} = \tfrac{2}{4} - \tfrac{1}{4} = \tfrac{1}{4}$. A quarter of a pizza is left.
72. Sam ate $\tfrac{2}{5}$ of a chocolate bar in the morning and $\tfrac{1}{5}$ in the evening. How much did he eat in total?
Answer: $\tfrac{2}{5} + \tfrac{1}{5} = \tfrac{3}{5}$. Three-fifths of the bar.
73. A water tank is $\tfrac{3}{4}$ full. It contains 60 litres. What is the capacity of the tank?
Answer: $\tfrac{3}{4}$ of capacity = 60 → capacity = 60 ÷ (3/4) = 60 × (4/3) = 80 litres.
74. Lily has 24 stickers. She gives away $\tfrac{1}{3}$ of them. How many stickers does she give away?
Answer: $\tfrac{1}{3} \times 24 = 8$. 8 stickers.
75. A class has 30 students. $\tfrac{2}{5}$ of them play football. How many play football?
Answer: $\tfrac{2}{5} \times 30 = 12$. 12 students.
76. A bag holds 48 marbles. $\tfrac{3}{8}$ are red, $\tfrac{1}{4}$ are blue, and the rest are green. How many marbles are green?
Answer: Red = $\tfrac{3}{8} \times 48 = 18$. Blue = $\tfrac{1}{4} \times 48 = 12$. Green = 48 − 18 − 12 = 18 marbles.
77. A recipe needs $\tfrac{2}{3}$ cup of sugar. Lily wants to bake $\tfrac{1}{2}$ of the recipe. How much sugar does she need?
Answer: $\tfrac{1}{2} \times \tfrac{2}{3} = \tfrac{2}{6} = \tfrac{1}{3}$. One-third cup.
78. A roll of ribbon is $4\tfrac{1}{2}$ metres long. Maya cuts off $1\tfrac{3}{4}$ metres. How much ribbon is left?
Answer: $4\tfrac{1}{2} - 1\tfrac{3}{4} = \tfrac{18}{4} - \tfrac{7}{4} = \tfrac{11}{4} = 2\tfrac{3}{4}$. 2¾ metres.
79. A pizza is cut into 8 slices. Sam eats $\tfrac{1}{4}$ of the pizza. How many slices does he eat?
Answer: $\tfrac{1}{4}$ of 8 = 2 slices.
80. Aria has $\tfrac{5}{6}$ of a litre of juice. She pours $\tfrac{1}{3}$ litre into a glass. How much juice is left in the bottle?
Answer: $\tfrac{5}{6} - \tfrac{1}{3} = \tfrac{5}{6} - \tfrac{2}{6} = \tfrac{3}{6} = \tfrac{1}{2}$. Half a litre.
81. Three friends share $\tfrac{3}{4}$ of a chocolate bar equally. How much does each get?
Answer: $\tfrac{3}{4} \div 3 = \tfrac{3}{4} \times \tfrac{1}{3} = \tfrac{1}{4}$. One-quarter of a bar each.
82. (Stretch.) A jug holds 1¾ litres of milk. Maya uses $\tfrac{2}{3}$ of the milk for baking. How much milk did she use?
Answer: $\tfrac{2}{3} \times \tfrac{7}{4} = \tfrac{14}{12} = \tfrac{7}{6} = 1\tfrac{1}{6}$. 1⅙ litres.
Decimal Word Problems (Problems 83–92)
83. Tom buys 2.5 kg of apples at $3 per kg. How much does he pay?
Answer: 2.5 × 3 = $7.50.
84. A ribbon is 4.6 m long. Maya cuts off 1.8 m. How much ribbon is left?
Answer: 4.6 − 1.8 = 2.8 m.
85. A bottle holds 1.5 litres of juice. How many litres are in 8 bottles?
Answer: 1.5 × 8 = 12 litres.
86. A car travels 45.6 km on 1 gallon of fuel. How far does it travel on 4.5 gallons?
Answer: 45.6 × 4.5 = 205.2 km.
87. A jar contains 3.75 kg of sugar. It is divided equally into 5 packets. How much sugar is in each packet?
Answer: 3.75 ÷ 5 = 0.75 kg.
88. Mia's grocery bill: bread $2.40, milk $3.25, eggs $4.80, butter $5.15. What is the total?
Answer: 2.40 + 3.25 + 4.80 + 5.15 = $15.60.
89. A pipe leaks 0.25 litres of water per minute. How many litres leak in 1 hour 30 minutes?
Answer: Time = 90 minutes. Leak = 0.25 × 90 = 22.5 litres.
90. A piece of cloth costs $12.75 per metre. How much does 6.4 metres cost?
Answer: 12.75 × 6.4 = $81.60.
91. A delivery van weighs 2.85 tonnes when empty and 4.62 tonnes when loaded. What is the weight of the cargo?
Answer: 4.62 − 2.85 = 1.77 tonnes.
92. (Stretch.) A factory produces 1,250 packets of biscuits per day. Each packet weighs 0.275 kg. How many kilograms of biscuits does the factory produce in a week (7 days)?
Answer: 1,250 × 0.275 = 343.75 kg per day. Weekly = 343.75 × 7 = 2,406.25 kg.
Percentage Word Problems (Problems 93–102)
93. A shirt costs $80. It is on 25% sale. What is the discount amount?
Answer: 25% × 80 = $20 discount.
94. Maya scored 18 out of 20 on a quiz. What percentage did she get?
Answer: $\tfrac{18}{20} \times 100 = $ 90%.
95. A school has 600 students. 40% of them are girls. How many girls are there?
Answer: 40% × 600 = 240 girls.
96. A laptop priced at $850 has 8% sales tax. What is the total cost including tax?
Answer: Tax = 0.08 × 850 = $68. Total = 850 + 68 = $918.
97. A coat originally priced at $120 is on 30% sale. What is the sale price?
Answer: Discount = 0.30 × 120 = $36. Sale price = 120 − 36 = $84.
98. A water tank is 75% full and contains 450 litres. What is the tank's full capacity?
Answer: 0.75 × capacity = 450 → capacity = 450 ÷ 0.75 = 600 litres.
99. A class has 32 students. 6 of them were absent today. What percentage was absent?
Answer: $\tfrac{6}{32} \times 100 = 18.75%$. 18.75% absent.
100. A book originally cost $40. The store raises the price by 15%. What is the new price?
Answer: Increase = 0.15 × 40 = $6. New = 40 + 6 = $46.
101. A factory produced 1,500 units last month. This month, production rose by 12%. How many units were produced this month?
Answer: Increase = 0.12 × 1,500 = 180. New total = 1,500 + 180 = 1,680 units.
102. (Stretch — successive percentages.) A shirt originally costs $100. It is given a 25% discount, and then an additional 10% off the discounted price. What is the final price?
Answer: After 25%: 100 × 0.75 = $75. After 10% on that: 75 × 0.90 = $67.50.
Ratio and Proportion Word Problems (Problems 103–110)
103. The ratio of boys to girls in a class is 3 : 4. If there are 21 boys, how many girls are there?
Answer: 3 : 4 = 21 : x → x = (21/3) × 4 = 28 girls.
104. A recipe uses sugar and flour in the ratio 2 : 5. If 8 cups of sugar are used, how much flour is needed?
Answer: 2 : 5 = 8 : x → x = (8/2) × 5 = 20 cups of flour.
105. $480 is shared between Maya and Tom in the ratio 5 : 3. How much does each get?
Answer: Total parts = 8. Each part = 480 ÷ 8 = 60. Maya gets 5 × 60 = $300. Tom gets 3 × 60 = $180. Maya: $300; Tom: $180.
106. A car travels 150 km in 2 hours. At the same rate, how far does it travel in 5 hours?
Answer: Rate = 150 ÷ 2 = 75 km/h. Distance in 5 h = 75 × 5 = 375 km.
107. If 4 workers can build a wall in 10 days, how many days will 8 workers (working at the same pace) take?
Answer: Total work = 4 × 10 = 40 worker-days. With 8 workers: 40 ÷ 8 = 5 days.
108. A map's scale is 1 : 200,000. If a road on the map is 6 cm long, what is its actual length in km?
Answer: Actual = 6 × 200,000 = 1,200,000 cm = 12 km.
109. The ratio of red to blue marbles in a bag is 3 : 5. If there are 56 marbles total, how many are red?
Answer: Total parts = 8. Each part = 56 ÷ 8 = 7. Red = 3 × 7 = 21 marbles.
110. (Stretch.) If 6 painters paint 3 walls in 4 days, how many days will 9 painters take to paint 6 walls (at the same rate)?
Answer: Painter-days per wall: (6 × 4) ÷ 3 = 8 painter-days/wall. For 6 walls: 8 × 6 = 48 painter-days. With 9 painters: 48 ÷ 9 ≈ 5.33 days (so it takes more than 5 days; round to 6 if discrete days are required).
Time Word Problems (Problems 111–118)
111. A bus leaves at 8:15 a.m. and arrives at 11:45 a.m. How long is the journey?
Answer: 11:45 − 8:15 = 3 hours 30 minutes.
112. Aria starts her homework at 4:20 p.m. and finishes at 6:05 p.m. How long did her homework take?
Answer: 6:05 − 4:20 = 1 hour 45 minutes.
113. A film starts at 7:30 p.m. and lasts 2 hours 25 minutes. What time does it end?
Answer: 7:30 + 2:25 = 9:55 p.m.
114. Maya needs to be at school by 8:00 a.m. The bus journey takes 35 minutes and she needs to leave home 15 minutes before the bus arrives. What time must she leave home?
Answer: Bus leaves at 8:00 − 0:35 = 7:25. Maya leaves home at 7:25 − 0:15 = 7:10 a.m.
115. A train leaves at 10:42 a.m. and arrives at 2:18 p.m. How long is the journey?
Answer: From 10:42 to 12:42 is 2 hours; from 12:42 to 2:18 is 1 hour 36 minutes. Total = 3 hours 36 minutes.
116. A factory operates 8.5 hours a day for 6 days a week. How many hours does it run in a week?
Answer: 8.5 × 6 = 51 hours.
117. Tom went to bed at 10:45 p.m. and woke up at 6:30 a.m. How long did he sleep?
Answer: 10:45 p.m. → midnight = 1 h 15 min. Midnight → 6:30 a.m. = 6 h 30 min. Total = 7 hours 45 minutes.
118. (Stretch — time-zone problem.) A flight leaves London at 11:00 a.m. (London time). The flight is 8 hours long. New York is 5 hours behind London. What is the New York local time when the flight lands?
Answer: Landing in London time = 11:00 a.m. + 8 h = 7:00 p.m. New York local time = 7:00 p.m. − 5 h = 2:00 p.m.
Money Word Problems (Problems 119–126)
119. Lily has 3 quarters, 4 dimes, and 7 pennies. How much money does she have in cents?
Answer: (3 × 25) + (4 × 10) + (7 × 1) = 75 + 40 + 7 = 122 cents ($1.22).
120. Sam buys 4 pencils at $1.25 each and 3 erasers at $0.75 each. How much does he pay?
Answer: (4 × 1.25) + (3 × 0.75) = 5.00 + 2.25 = $7.25.
121. Maya has $25. She buys a book for $12.50 and a pen for $3.75. How much change does she have left?
Answer: 25 − 12.50 − 3.75 = $8.75.
122. A movie ticket costs $15 for adults and $9 for children. A family with 2 adults and 3 children goes to the movie. How much do they pay?
Answer: (2 × 15) + (3 × 9) = 30 + 27 = $57.
123. Maya saves $45 each month. How much will she save in 1 year?
Answer: $45 × 12 = $540.
124. A meal costs $48. The family adds a 18% tip. How much is the tip?
Answer: 0.18 × 48 = $8.64.
125. Aria invests $1,000 at 5% simple interest per year. How much interest does she earn in 3 years?
Answer: Interest = 1,000 × 0.05 × 3 = $150.
126. (Stretch — compound interest.) Tom deposits $2,000 at 4% compound interest per year, compounded annually. How much is in the account after 2 years?
Answer: Year 1: 2,000 × 1.04 = $2,080. Year 2: 2,080 × 1.04 = $2,163.20.
Measurement Word Problems (Problems 127–134)
127. A roll of ribbon is 4 metres long. Maya cuts off 145 cm. How much ribbon is left? (in cm)
Answer: 4 m = 400 cm. 400 − 145 = 255 cm.
128. A car weighs 1,250 kg. After loading luggage, the car weighs 1.6 tonnes. What is the weight of the luggage?
Answer: 1.6 t = 1,600 kg. Luggage = 1,600 − 1,250 = 350 kg.
129. A bottle holds 1.5 litres. A glass holds 250 ml. How many full glasses can the bottle fill?
Answer: 1.5 L = 1,500 ml. 1,500 ÷ 250 = 6 glasses.
130. A rectangular pool is 12 m long and 6 m wide. What is its perimeter?
Answer: Perimeter = 2(12 + 6) = 36 m.
131. Lily ran 3.2 km on Monday, 4.5 km on Tuesday, and 5.1 km on Wednesday. How far did she run in total?
Answer: 3.2 + 4.5 + 5.1 = 12.8 km.
132. A water bucket holds 8 litres. The tap fills it at 200 ml per second. How long does it take to fill?
Answer: 8 L = 8,000 ml. Time = 8,000 ÷ 200 = 40 seconds.
133. A rope is 5.4 m long. Tom cuts it into 9 equal pieces. How long is each piece (in cm)?
Answer: 5.4 m = 540 cm. 540 ÷ 9 = 60 cm.
134. (Stretch — area and unit conversion.) A rectangular farm is 250 m × 180 m. What is its area in hectares? (1 hectare = 10,000 m²)
Answer: Area in m² = 250 × 180 = 45,000 m². In hectares = 45,000 ÷ 10,000 = 4.5 hectares.
Geometry Word Problems (Problems 135–142)
135. A rectangle has length 12 cm and width 8 cm. What is its area?
Answer: 12 × 8 = 96 cm².
136. A square has perimeter 28 cm. What is its side length?
Answer: 28 ÷ 4 = 7 cm.
137. A triangle has a base of 14 cm and a height of 9 cm. What is its area?
Answer: $\tfrac{1}{2} \times 14 \times 9 = $ 63 cm².
138. A circular garden has radius 7 m. What is its area? (Use π ≈ 22/7)
Answer: Area = π r² = (22/7) × 49 = 22 × 7 = 154 m².
139. A rectangular box is 8 cm × 5 cm × 6 cm. What is its volume?
Answer: 8 × 5 × 6 = 240 cm³.
140. A cube has edge length 5 cm. What is its surface area?
Answer: 6 × 5² = 6 × 25 = 150 cm².
141. A right triangle has legs 6 cm and 8 cm. What is the hypotenuse?
Answer: Pythagoras: $c^2 = 6^2 + 8^2 = 36 + 64 = 100$ → $c = $ 10 cm.
142. (Stretch.) A cylinder has radius 7 cm and height 10 cm. What is its volume? (Use π ≈ 22/7)
Answer: Volume = π r² h = (22/7) × 49 × 10 = 1,540 cm³.
Probability and Data Word Problems (Problems 143–147)
143. A bag has 5 red marbles and 3 blue marbles. What is the probability of drawing a red marble?
Answer: $\tfrac{5}{8}$ = 5/8 (or 62.5%).
144. A spinner has 4 equal sections: red, blue, green, yellow. What is the probability of landing on red?
Answer: $\tfrac{1}{4}$ = 1/4 (25%).
145. A standard die is rolled. What is the probability of rolling an even number?
Answer: Even outcomes: 2, 4, 6 = 3 of 6 → $\tfrac{3}{6} = \tfrac{1}{2}$ = 50%.
146. A class of 30 students has the following heights (in cm): five 140s, ten 145s, eight 150s, seven 155s. What is the mean height?
Answer: Sum = 5(140) + 10(145) + 8(150) + 7(155) = 700 + 1,450 + 1,200 + 1,085 = 4,435. Mean = 4,435 ÷ 30 = 147.83 cm.
147. (Stretch.) A bag has 6 red, 4 blue, and 5 green balls. One ball is drawn at random. What is the probability it is NOT green?
Answer: Total = 15. Not green = 6 + 4 = 10. Probability = $\tfrac{10}{15} = \tfrac{2}{3}$ = 2/3 (about 66.7%).
Algebra / Variable Word Problems (Problems 148–155)
148. If 3 times a number plus 5 equals 20, what is the number?
Answer: $3x + 5 = 20$ → $3x = 15$ → $x = $ 5.
149. Tom is 4 years older than Maya. The sum of their ages is 18. How old is each?
Answer: Maya = $x$. Tom = $x + 4$. $x + (x + 4) = 18$ → $2x = 14$ → $x = 7$. Maya is 7; Tom is 11.
150. A rectangle's length is 4 cm more than its width. Its perimeter is 28 cm. Find length and width.
Answer: Width = $w$. Length = $w + 4$. $2[(w + 4) + w] = 28$ → $4w + 8 = 28$ → $w = 5$. Width = 5 cm; Length = 9 cm.
151. Aria spent half her money on a book and $5 on lunch. She has $25 left. How much did she start with?
Answer: Start = $x$. $x - \tfrac{x}{2} - 5 = 25$ → $\tfrac{x}{2} = 30$ → $x = $ $60.
152. Twice a number minus 7 equals 23. Find the number.
Answer: $2x - 7 = 23$ → $2x = 30$ → $x = $ 15.
153. A father is 3 times as old as his son. In 10 years, the father will be twice as old as the son. How old are they now?
Answer: Son = $x$. Father = $3x$. In 10 years: $3x + 10 = 2(x + 10)$ → $3x + 10 = 2x + 20$ → $x = 10$. Son is 10; father is 30.
154. A two-digit number has tens digit 3 more than the units digit, and the sum of the digits is 11. Find the number.
Answer: Units = $u$, tens = $u + 3$. $u + (u + 3) = 11$ → $u = 4$. Number = 74.
155. (Stretch — system of equations.) Two notebooks and three pens cost $13. Three notebooks and two pens cost $14. Find the cost of each.
Answer: Let $n$ = notebook, $p$ = pen. $2n + 3p = 13$ and $3n + 2p = 14$. Multiply first by 3: $6n + 9p = 39$. Multiply second by 2: $6n + 4p = 28$. Subtract: $5p = 11$ → $p = $ $2.20. Then $2n + 3(2.20) = 13$ → $2n = 6.40$ → $n = $ $3.20.
How to Use This Collection With Your Child
Three ways parents have used these problems with the best results:
Daily 5. Pick five problems from a single category (one per day for a week). Same topic, gradually harder. Builds depth.
Weekly review. Pick 10 problems across three different topics for a weekly review session. Builds breadth and the ability to recognise the operation needed.
Practice-test format. Choose 20 mixed problems and time the session. Stops at 30 minutes regardless of completion. Builds endurance + identifies which categories need more practice.
For children who freeze on word problems: start in the Easy section of any topic, not the Stretch ones. Confidence first, complexity second.
Signs Your Child Is Struggling With Word Problems
Two or more of these consistently signals it's time to focus specifically on word problems:
Computes arithmetic correctly but freezes when the same calculation is wrapped in words.
Reads the problem but immediately starts computing without identifying what's being asked.
Always picks the wrong operation (adds when they should multiply, subtracts when they should divide).
Can solve one problem but cannot solve the same problem with different numbers.
Says "I don't know where to start" — every time.
Avoids word problems on homework, prefers calculation problems.
These are signals — not verdicts. The interventions in the How to Use This Collection section above address all six.
When to Bring In Outside Help
Three thresholds where outside help moves from optional to recommended:
Word-problem performance is significantly below calculation performance — and 4–6 weeks of consistent home practice (using collections like this one) hasn't closed the gap.
Anxiety has formed around word problems specifically — your child can do math but emotionally shuts down on word problems.
Word problems are blocking grade-level performance — failing exams not because the math is hard but because the questions are word-based.
A program that teaches word-problem translation (English to equation) — not just calculation — closes this gap fastest.
How Bhanzu Approaches This
Bhanzu's curriculum treats word-problem translation as a teachable skill — separate from arithmetic. Every session includes translation practice before any pure calculation. The Level 0 diagnostic at the start of every Bhanzu journey screens for word-problem performance separately from calculation, so we can place a child at their actual word-problem level (often different from their school grade in this specific skill).
The method: WHY-first, then translate, then solve. We open with a real situation, build the equation from the situation, then solve. The procedure follows the WHY. Students who learn this way handle exam word problems they've never seen before — because they're translating, not memorising solution patterns.
Live online classes with peers from 20+ countries; in-person at our McKinney, TX center for Dallas-Fort Worth families.
Fit signal. Bhanzu fits parents whose child has word-problem anxiety or word-problem performance below calculation performance — and who can commit to a structured curriculum that treats translation as a separate skill. Not the right fit for families looking for one-off homework rescue.
Book a free demo class — the trainer assesses your child's word-problem performance specifically and shows you where the gap actually sits.
Key Takeaways
155 worked word problems organised across 15 topics — addition through algebra.
The UPSCC method (Understand → Plan → Solve → Check → Communicate) is the universal framework — works on every problem at every grade.
Word problems are translation problems — turning English into a math sentence is the underlying skill.
Consistency over intensity — 10–15 minutes a day beats 90 minutes on weekends.
Start in Easy sections if your child has anxiety; build confidence before complexity.
A Three-Move Practice Plan for This Week
Three moves to start this week.
Today, pick one category your child is least confident in. Have them try problems 1–3 of that category from the list above. Use the UPSCC method explicitly.
This week, do five problems a day from the same category. Same topic, gradually harder.
At week-end, do five problems from three different topics mixed together. This builds the "which operation?" recognition skill — the heart of word-problem competence.
Want a Bhanzu trainer to assess your child's word-problem performance separately from their calculation skill — and show you exactly where the gap sits? Book a free demo class — online globally, or in person at our McKinney, TX center.
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