Linear Word Problems Worksheet
Word problems can be a great way to practice applying mathematical concepts to real-world situations. In this worksheet, we’ll focus on linear word problems, which involve solving equations to find the unknown value.
📝 Note: Read each problem carefully and use the given information to solve for the unknown variable.
Problem 1:
Tom has been saving money for a new bike and has 120 in his savings account. He wants to buy a bike that costs 180. Tom’s parents have agreed to give him an allowance of $5 per week for doing chores. How many weeks will it take Tom to have enough money to buy the bike?
Let x be the number of weeks. The equation can be set up as 120 + 5x = 180.
Solution:
| Step | Equation |
|---|---|
| 1 | 120 + 5x = 180 |
| 2 | 5x = 180 - 120 |
| 3 | 5x = 60 |
| 4 | x = 60 / 5 |
| 5 | x = 12 |
Answer: It will take Tom 12 weeks to have enough money to buy the bike.
Problem 2:
A bakery sells a total of 250 loaves of bread per day. They sell a combination of whole wheat and white bread. If the number of whole wheat loaves sold is 30 more than the number of white bread loaves sold, and the total number of white bread loaves sold is x, how many whole wheat loaves are sold?
Let x be the number of white bread loaves. The equation can be set up as x + (x + 30) = 250.
Solution:
| Step | Equation |
|---|---|
| 1 | x + (x + 30) = 250 |
| 2 | 2x + 30 = 250 |
| 3 | 2x = 250 - 30 |
| 4 | 2x = 220 |
| 5 | x = 220 / 2 |
| 6 | x = 110 |
Answer: The number of whole wheat loaves sold is x + 30 = 110 + 30 = 140.
Problem 3:
Ashley is planning a road trip from City A to City B. The distance between the two cities is 240 miles. If she drives at an average speed of 40 miles per hour, how many hours will it take her to reach City B?
Let x be the number of hours. The equation can be set up as 40x = 240.
Solution:
| Step | Equation |
|---|---|
| 1 | 40x = 240 |
| 2 | x = 240 / 40 |
| 3 | x = 6 |
Answer: It will take Ashley 6 hours to reach City B.
Problem 4:
A group of friends want to share some candy equally. If they have 48 pieces of candy and there are 8 friends, how many pieces of candy will each friend get?
Let x be the number of pieces each friend gets. The equation can be set up as 8x = 48.
Solution:
| Step | Equation |
|---|---|
| 1 | 8x = 48 |
| 2 | x = 48 / 8 |
| 3 | x = 6 |
Answer: Each friend will get 6 pieces of candy.
Problem 5:
A bookshelf has 5 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many books can be placed on it in total?
Let x be the total number of books. The equation can be set up as 5 x 8 = x.
Solution:
| Step | Equation |
|---|---|
| 1 | 5 x 8 = x |
| 2 | x = 5 x 8 |
| 3 | x = 40 |
Answer: The bookshelf can hold a total of 40 books.
What is a linear equation?
+
A linear equation is an equation in which the highest power of the variable(s) is 1.
How do I solve a linear equation?
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To solve a linear equation, isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
What is the purpose of solving linear equations?
+
Solving linear equations helps us find the value of the unknown variable, which can be used to solve real-world problems.
The key to solving linear word problems is to read the problem carefully, identify the unknown variable, and set up an equation to represent the situation. By solving the equation, we can find the value of the unknown variable and answer the question.
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