Question

A woman bought some large frames for $19 each and some small frames for $9 each at a closeout sale. If she bought 18 frames for $222, find how many of each type she bought.

Answer 1

Answer: 6 large frames and 12 small frames

Explanation:

We define the following:

x = number of large frames

y = number of small frames

Make the following equations:

x + y = 18

19x + 9y = 222

Use system of equations to solve. We find the value of x first.

y = 18 - x

⇒ 19x + 9(18 - x) = 222

⇒ 19x + 162 - 9x = 222

⇒ 10x + 162 = 222

⇒ 10x = 60

⇒ x = 6

Find value of y:

6 + y = 18

y = 12

∴ 6 large frames and 12 small frames were purchased.