A woman bought some large frames for $19 each and some small frames for $7 each at a closeout sale. If she bought 22 frames for $226, find how many of each type she bought. She bought large frames.

The number of each type of large frames and small frames bought is 6 and 16 respectively.

Given:

cost of large frames = $19

cost of small frames = $7

Total cost = $226

let

large frames = x

small frames = y

x + y = 22 (1)

19x + 7y = 226 (2)

multiply (1) by 7

7x + 7y = 154 (3)

19x + 7y = 226 (2)

subtract (3) from (2)

19x - 7x = 226 - 154

12x = 72

x =72/12

x = 6

substitute x = 6 into (1)

x + y = 22 (1)

6 + y = 22

y = 22 - 6

y = 16

Therefore, number of each type of large frames and small frames bought is 6 and 16 respectively.

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6 large frames and 16 small frames.

Step-by-step explanation:

Make a system of equations, where l is the number of large frames and s is the number of small frames:

l + s = 22

19l + 7s = 226

Solve by elimination by multiplying the top equation by -7:

-7l - 7s = -154

19l + 7s = 226

12l = 72

l = 6

Plug 6 in as l into the first equation, and solve for s:

l + s = 22

6 + s = 22

s = 16

So, she bought 6 large frames and 16 small frames.