1.8 Writing and Solving Equations

The world is full of word problems. How much dessert do I need to make for the party? Should I fly or drive to my family reunion? How much money do I need to fill the car with gas? How much of a tip should I leave at a restaurant? How many socks should I pack for vacation? How many pounds of potatoes should I buy for Thanksgiving dinner, and what time do I need to put them in the oven?

Setting up an equation, and then solving for the unknown can help us find the answer to these types of questions. To help guide you when setting up and solving a word problem, refer to the list below.

Table 1.8.1
Property or Steps
Step 1: Read the problem. Make sure you understand all the words and ideas.

Step 2: Identify what you are looking for.

Step 3: Set a variable equal to the unknown.

Step 4: Write an equation to represent the situation.

Step 5: Solve the equation using algebra.

Step 6: Verify your solution, and make sure it makes sense.

Step 7: Answer the question with a complete sentence.
Example 1

Pilar bought a purse on sale for $18, which is half the original price. What was the original price of the purse?

Table 1.8.2
Steps Solution
Identify what you are looking for and set a variable equal to the unknown. p = the original price of the purse
Write an equation to represent the situation. \frac{p}{2}=18
Solve the equation using algebra. 2 \bullet \frac{p}{2}=2 \bullet 18

p = 36
Verify your solution, and make sure it makes sense. \frac{36}{2}=18

18=18
Answer the question with a complete sentence. The original price of the purse was $36.
Practice 1

Solve the following word problems.

a) The Robles family has two dogs, Buster and Chandler. Together, they weigh 71 pounds. Chandler weighs 28 pounds. How much does Buster weigh?

 

 

 b) Shayla paid $24 575 for her new car. This was $875 less than the sticker price. What was the sticker price of the car?

 

 
c) The difference of a number and 6 is 13. Find the number.

 

 

 

 d) The sum of twice a number and 7 is 15. Find the number.

 

 

 
e) Joaquin bought a bookcase on sale for $120, which was two-thirds of the original price. What was the original price of the bookcase?

 

 

 

 f) One number is 5 more than another. The sum of the numbers is 21. Find the numbers.

 

 

 
g) Jamal did Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is 8 more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?

 

 

Homework 

  1. Solve.

    a) The Pappas family has two cats, Zeus and Athena. Together, they weigh 13 pounds. Zeus weighs 6 pounds. How much does Athena weigh?

     

     

    		 b) Angela and Nikolay are roommates. Together, they have 68 books. Angela has 26 books. How many books does Nikolay have?

     

     
    c) Micah paid $19 875 for his new car. This was $1 025 less than the sticker price. What was the sticker price of the car?

     

     

    		 d) The admission price to a movie during the day is $7.75. This is $3.25 less than the price at night. How much does the movie cost at night?

     

     
    e) Carissa read a total of 54 pages in her English and Psychology textbooks. She read 41 pages in her English textbook. How many pages did she read in her Psychology textbook?

     

     

    		 f) Malia’s temperature was 0.7 degrees higher this morning than it had been last night. Her temperature this morning was 101.2 degrees. What was her temperature last night?

     

     
    g) Deon’s daughter is 5 years younger than his son. Deon’s son is 12 years old. How old is his daughter?

     

     

     

    		 h) Owen’s paycheque this week was $17.43 less than his paycheque last week. His paycheque this week was $103.76. How much was Owen’s paycheque last week?

     

     

     

  2. Solve.

    a) Two-fifths of the songs in Mariel’s playlist are country. If there are 16 country songs, what is the total number of songs in the playlist?

     

     

     

    		 b) Two-thirds of the people in an outdoors club are adults, and the other one-third are children. If there are 20 adults, what is the total number of people in the club?

     

     

     
    c) Kaya has 25 country music CDs, which is one-fifth of her CD collection. How many CDs does Kaya have?

     

     

     

    		 d) The difference of a number and 8 is 17. Find the number.

     

     

     
    e) The difference of a number and 11 is –7. Find the number.

     

     

     

    		 f) The sum of a number and 8 is 12. Find the number.

     

     

     
    g) The sum of four times a number and 2 is 14. Find the number.

     

     

     

    		 h) The sum of three times a number and 7 is 25. Find the number.

     

     

     
    i) The sum of three times a number and 8 is 23. Find the number.

     

     

     

    		 j) One number is 6 more than another. The sum of the numbers is 24. Find the numbers.

     

     

     
    k) The sum of two numbers is 58. One number is 4 more than the other. Find the numbers.

     

     

     

    		 l) One number is 6 more than the other. Their sum is 42. Find the numbers.

     

     

     
    m) Ginny and her classmates formed a study group. The number of 16-year-olds in the study group was 3 more than twice the number of 15-year-olds. There were 11 16-year-olds in the study group. How many 15-year-olds were in the study group?

     

     
    n) Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 more than twice the number of notebooks. He bought 7 textbooks. How many notebooks did he buy?

     

     
    o) There are 16 dogs at the vet clinic. The number of dogs is 4 more than twice the number of cats. Find the number of cats.

     

     
    p) Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?

     

     
    q) Laurie has $46 000 invested in stocks and bonds. The amount invested in stocks is $8 000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?

     

     
    r) A married couple together earns $110 000 per year. The husband earns $16 000 less than twice what his wife earns. How much does the wife earn?

     

     
    s) The Canadian Real Estate Association (CREA) data shows that the median price of new home in the Canada in December 2018 was $470 000. This was $14 000 more than 19 times the price in December 1967. What was the median price of a new home in December 1967?

     

     
    t) Patti paid $35 for a purse on sale for $10 off the original price. What was the original price of the purse?

     

     
    u) Minh spent $6.25 on five identical sticker books to give his nephews. Find the cost of each sticker book.

     

     
    v) One number is 1 more than twice another. Their sum is –5. Find the numbers.

     

     
    w) The sum of two numbers is 14. One number is 2 less than three times the other. Find the numbers.

     

     
    x) Lania is lining up children’s and adult bicycles at the bike shop where she works. The number of children’s bicycles is 9 less than three times the number of adult bicycles. There are 42 adult bicycles. How many children’s bicycles are there?

     

     

     

  3. A group of 40 people went on a nature trip. The group included both adults and children. The number of children was 5 less than twice the number of adults. How many adults and how many children went on the trip?

    a) 10 adults, 30 children
    b) 15 adults, 25 children
    c) 20 adults, 20 children
    d) 12 adults, 28 children

  4. There are 40 insects in a garden. The number of bees is 4 more than twice the number of butterflies. How many bees and how many butterflies are in the garden?

    a) 28 bees, 15 butterflies
    b) 32 bees, 14 butterflies
    c) 28 bees, 12 butterflies
    d) 48 bees, 12 butterflies

  5. In a garden, there are two types of plants: sunflowers and daisies. The number of sunflowers is 4 more than twice the number of daisies. If the total number of plants in the garden is 52, how many sunflowers and how many daisies are there?

    a) 36 sunflowers, 16 daisies
    b) 32 sunflowers, 14 daisies
    c) 26 sunflowers, 12 daisies
    d) 28 sunflowers, 10 daisies

Answers

1.

a) 7 b) 42 c) $20 900 d) $11.00
e) 13 f) 100.5 degrees g) 7 h) $121.19

2.

a) 40 b) 30 c) 125 d) 25 e) 4 f) 4
g) 3 h) 6 i) 5 j) 9, 15 k) 27, 31 l) 18, 24
m) 4 n) 2 o) 6 p) 58 q) $13 500 r) $42 000
s) $24 000 t) $45 u) $1.25 v) -2,-3 w) 4, 10 x) 117
3. b 4. c 5. a

Attribution

Unless otherwise indicated, material on this page has been adapted from the following resource:

Mazur, I. (2021). Introductory algebra. BCcampus. https://collection.bccampus.ca/textbooks/intermediate-algebra-bccampus-412/, licensed under CC BY 4.0

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Math 10C Workbook Copyright © 2026 by Leanne Thompson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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