Question

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.

Answer 1

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

Answer 2

Answer:

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