Math Help: 7th Grade Equations

By 7th grade, most students already know how to solve 1-step equations with rational numbers. Now, you'll focus on writing equations to represent and solve real-world problems. Read on for examples that show how to solve word problems using algebra!

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How to Solve Equations for 7th Grade

While you may have written simple, 1-step equations before, now you'll use equations to represent problems with multiple steps. To solve problems like these, you'll need to identify the variable and determine how it relates to the other information given in the problem.

Solving Word Problems

Example One

Many word problems require you to write and solve an equation that looks like this: ax + b = c. In this equation x represents the variable, and a, b and c are quantities given in the problem. Here's an example:

Mrs. Sanders buys tomatoes at a local farmers' market. Each tomato costs $0.50. On one trip, she paid a total of $35, which included $5 for a basket to carry her produce. What is the total number of tomatoes that Mrs. Sanders purchased on her trip?

The variable, x, represents the number of tomatoes that Mrs. Sanders bought. The problem states that she paid $0.50 for each tomato, so the total cost for the tomatoes is calculated by multiplying that price by x (0.50x). To get the total amount that Mrs. Sanders paid, you'll need to add on the cost of the basket ($5), which gives you the expression 0.50x + 5. Since the problem tells you that Mrs. Sanders paid $35 altogether, you can write the equation 0.50x + 5 = 35. Then, find the value of x, like this:

0.50x + 5 = 35

0.50x + 5 - 5 = 35 - 5

0.50x = 30

(0.50x) ÷ 0.50 = 30 ÷ 0.50

x = 60

Example Two

Another type of word problem you'll encounter frequently is the kind that can be represented in this format: a(x + b) = c. Here's an example:

Francine bought a pencil and a notebook at the store. The notebook cost $1.85. She paid sales tax of $0.10, or 5% of her total purchase. How much did Francine's pencil cost?

The cost of Francine's pencil is represented by the variable, x. By adding that to the cost of the notebook, you get the total amount of her purchase (x + 1.85). To calculate the 5% sales tax that Francine paid, multiply 0.05 by the total amount of her purchase, like this: 0.05(x + 1.85). Since you know the sales tax was $0.10, you can write the equation 0.05(x + 1.85) = 0.10. Here's the solution:

0.05(x + 1.85) = 0.10

0.05(x + 1.85) ÷ 0.05 = 0.10 ÷ 0.05

x + 1.85 = 2

x + 1.85 - 1.85 = 2 - 1.85

x = 0.15

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