Like Terms and More on Solving Equations

Combining Like Terms in Equations

Solve the following problem.

Adrian bought three shirts and one pair of pants. After arriving at home, Adrian decided she wanted two more shirts and went back to the store to buy them. Adrian spent a total of $299. If Adrian paid $69 for the pants, what was the cost of each shirt?

We set up the equation similar to the first opening problem, but we also account for the second purchase. Let x represent the cost of one shirt. Adrian would have paid 3x + 69 for three shirts and one pair of pants and 2x for the two shirts. Putting these two values together, we see that we need to solve the equation 3x + 69 + 2x = 299 for x. This equation has two terms with the variable x. How would we combine these two terms and solve the equation?

First, we use the associative and commutative properties of addition to rewrite the equation

3x + 2x + 69 = 299.

Next, use the Distributive Property of Multiplication over Addition to rewrite the equation

(3 + 2)x + 69 = 299.

Adding 2 and 3, we obtain

5x + 69 = 299.

Finish solving the equation as before

(5x + 69) – 69 = 299 – 69

5x = 230

(5x) ÷ 5 = 230 ÷ 5

x = 46

Each shirt cost Adrian $46.

Notice that we used the distributive property to combine the two terms that had the variable x. The distributive property is the key to combining expressions with like terms.

Self-Check Problem

Eric bought three pairs of socks and two T-shirts in one store and two pairs of socks in another store. Each T-shirt cost $12 and Eric spent a total of $54. What was the average price Eric paid for a pair of socks?

Solution

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