Question

A woman bought some large frames for $12 each and some small frames for $4 each at a closeout sale. If she bought 10 frames for $64, find how many of each type she bought.

a. 3 large frames and 7 small frames
b. 5 large frames and 5 small frames
c. 6 large frames and 4 small frames
d. 7 large frames and 3 small frames

Answer 1

The woman bought 3 large frames and 7 small frames. This was determined by setting up a system of equations based on the number of frames and the total cost, then solving for the number of large and small frames.

Step-by-step explanation:

To find out how many of each type of frame the woman bought, we can set up a system of equations. Let L be the number of large frames and S be the number of small frames. We have two pieces of information that can be turned into equations:

• The total number of frames bought was 10: L + S = 10.
• The total amount spent was $64: 12L + 4S = 64.

We can solve this system using the substitution or elimination method. If we subtract the first equation from the second equation, multiplied by 4, we get:

12L + 4S = 64
(4 × (L + S = 10)) → 4L + 4S = 40
Subtracting these equations gives us: 8L = 24, so L = 3.

Using L = 3 in the first equation, we get: 3 + S = 10, so S = 7.

Therefore, the woman bought 3 large frames and 7 small frames.