Word Problems Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Word Problems.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Word problems require translating a real-world scenario described in natural language into mathematical relationships, identifying the unknown quantity, setting up equations or expressions, and solving them to answer the question.

You are decoding a story into variables, equations, and constraints.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A word problem turns a real-world scenario into variables, expressions, and equations, then solves for the unknown the question names.

Common stuck point: The procedure for word problems is the easy part; the trap is operating on numbers before modeling. Asking "Must I translate a worded scenario into an equation or expression before I can compute?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Must I translate a worded scenario into an equation or expression before I can compute?

Worked Examples

Example 1

easy
Maria had 45 stickers. She gave 12 to her friend and then bought 20 more. How many stickers does she have now?

Answer

53 stickers53 \text{ stickers}

First step

1
Start with the initial amount: Maria has 45 stickers.

Full solution

  1. 2
    After giving away 12, subtract: 45−12=3345 - 12 = 33.
  2. 3
    After buying 20 more, add: 33+20=5333 + 20 = 53.
Translate each action in the story into a mathematical operation: 'gave away' means subtract, 'bought more' means add. Perform operations in chronological order.

Example 2

medium
A rectangular garden has a perimeter of 56 metres. If the length is 3 metres more than twice the width, find the dimensions.

Example 3

medium
A shirt costs $24\$24 after a 20%20\% discount. What was the original price?

Example 4

medium
A class of 30 students has 18 girls. What is the ratio of girls to boys?

Example 5

hard
A rectangle's length is 22 more than its width. Its perimeter is 2424 cm. Find its area.

Example 6

hard
The sum of four consecutive even integers is 108108. Find the smallest.

Example 7

challenge
A boat goes 2020 km downstream and back upstream in 55 hours. The current is 33 km/h. Find the boat's speed in still water.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A baker makes 8 trays of muffins with 12 muffins per tray. He sells all but 15. How many muffins were sold?

Example 2

hard
Two trains leave the same station at the same time, travelling in opposite directions. One train travels at 65 km/h and the other at 85 km/h. After how many hours will they be 450 km apart?

Example 3

easy
Tom has 5 apples and buys 8 more. How many apples does he have now?

Example 4

easy
A ribbon is 24 cm long and is cut into 4 equal pieces. How long is each piece?

Example 5

easy
A box holds 6 cans. How many cans are in 7 boxes?

Example 6

easy
Sara had 20 stickers and gave away 7. How many are left?

Example 7

easy
A pencil costs $2\$2. How much do 9 pencils cost?

Example 8

easy
There are 15 boys and 12 girls in a class. How many students in all?

Example 9

easy
A jug holds 3 liters. How many liters do 5 identical jugs hold?

Example 10

easy
A movie is 120 minutes long. How many hours is that?

Example 11

medium
A store sells shirts for $15\$15 each. With a coupon, the total for some shirts is $60\$60. How many shirts were bought?

Example 12

medium
A rectangle has length 12 cm and area 96 cm2^2. Find its width.

Example 13

medium
Maria is 3 times as old as her brother. The sum of their ages is 24. How old is the brother?

Example 14

medium
A train leaves at 2:15 PM and arrives at 5:00 PM. How long is the trip in minutes?

Example 15

medium
A phone costs $200\$200 after a 20% discount. What was the original price?

Example 16

medium
Pencils come in packs of 12. A teacher needs 100 pencils. How many packs must be bought?

Example 17

medium
A car travels 240 km in 3 hours, then 180 km in 2 hours. What is the average speed for the whole trip?

Example 18

medium
A book has 320 pages. Sam reads 40 pages a day. How many days to finish?

Example 19

medium
A parking lot charges $3\$3 for the first hour and $2\$2 for each additional hour. What is the cost for 5 hours?

Example 20

challenge
Adult tickets are $8\$8 and child tickets $5\$5. 12 tickets were sold for $81\$81 total. How many adult tickets?

Example 21

challenge
A tank is filled by a pipe in 6 hours and drained by another in 9 hours. With both open, how long to fill the empty tank?

Example 22

challenge
The sum of three consecutive integers is 72. Find the largest.

Example 23

easy
A library had 84 books. It received a shipment of 36 more. How many books are in the library now?

Example 24

easy
Jamal had 75 marbles and lost 28. How many marbles does he have left?

Example 25

easy
A book has 150 pages. Lena read 65 pages. How many pages are left to read?

Example 26

easy
A bag of rice weighs 5 kg. How many kg do 14 bags weigh?

Example 27

medium
A school orders 24 boxes of pencils. Each box has 12 pencils. They give out 200 pencils. How many pencils are left?

Example 28

medium
A rectangular field is 3030 m by 1818 m. Find its perimeter and area.

Example 29

medium
A car travels 150150 km in 22 hours, then another 9090 km in 11 hour. What is its average speed for the whole trip?

Example 30

medium
A recipe needs 34\tfrac{3}{4} cup of sugar for one batch. How much sugar is needed for 5 batches?

Example 31

medium
Train A leaves Station 1 at 60 km/h. Train B leaves the same station 1 hour later at 80 km/h, in the same direction. After how many more hours will B catch up to A?

Example 32

medium
Tickets cost $12\$12 for adults and $7\$7 for children. 8 tickets cost $76\$76 total. How many adult tickets were sold?

Example 33

medium
A swimming pool fills at 2424 liters/min. How long to fill a 14401440-liter pool?

Example 34

medium
A taxi charges $4\$4 plus $2\$2 per km. What is the fare for a 77-km ride?

Example 35

hard
A jar contains nickels ($0.05) and quarters ($0.25). There are 22 coins worth $3.10\$3.10 in total. How many quarters are there?

Example 36

hard
Two pipes can fill a tank in 44 and 66 hours respectively. Working together, how long do they take?

Example 37

hard
A merchant marks up a phone by 30%30\%, then offers a 10%10\% discount on the marked price. If the original cost was $200\$200, what is the final selling price?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

algebraic representationmodeling with equationsproportional reasoning