Karen karlin bought some large frames for $15 each and some small frames for $8 each at a closeout sale. if she bought 22 frames for $239, find how many of each type she bought.

small frames ($8) : s

large frames ($15) : L

Cost: 8s + 15L = 239 ⇒ 1 (8s + 15L = 239) ⇒ 8s + 15L = 239

Quantity: s + L = 22 ⇒ - 8 (s + L = 22) ⇒ - 8s - 8 L = - 176

7L = 63

L = 9

Quantity: s + L = 22 ⇒ s + (9) = 22 ⇒ s = 13

Answer: 13 small frames, 9 Large frames

9 large frames and 13 small frames

Step-by-step explanation:

Then number of each type can be found simultaneously by interpreting the given statements into equations. As such, if the number of the large frames and small frames purchased are a and b respectively. if she bought 22 frames then,

a + b = 22

Furthermore, if Karen karlin bought some large frames for $15 each and some small frames for $8 each at a closeout sale for $239 then

15a + 8b = 239

solving both simultaneously,

b = 22 - a

15a + 8 (22 - a) = 239

15a - 8a + 176 = 239

7a = 239 - 176

7a = 63

a = 9

b = 22 - 9

= 13