Question

A woman bought some large frames for ​$10 each and some small frames for ​$5 each at a closeout sale. If she bought 27 frames for ​$​180, find how many of each type she bought. She bought ____ large frames.

Answer 1

Explanation:

This is a guessing game. You assume how much there is, and then you check. I was led to the conclusion that there are 9 large frames and 18 small frames.

Answer 2

She bought 9 large frames

Explanation:

Create a system of two equations and two unknowns (the number of small frames that we call S, and the number of large frames that we call L).

The two equations become:

(a) L + S = 27 (since she bought 27 frames total)

(b) 10 L + 5 S = 180

Now, let's solve for S in the first equation: S = 27 - L

ad use it to replace for S in equation (b):

10 L + 5 (27 - L) = 180

10 L - 5 L + 135 = 180

5 L = 180 - 135

5 L = 45

L = 9

Therefore she bought 9 large frames