Sarah went to an electronics store, purchased 3 CDs and 5 DVDs, and spent $137. Michelle went to the same store, bought 2 CDs and 7 DVDs, and spent $161. How much does each CD sell for at the store?

Question

insa · Answer

Let the cds= x
then the dvds= y
3x+5y=137______ 1
2x+7y= 161__________2
2(3x+5y)= 2(137)
6x+10y= 274________ 3
3(2x+7y)=3(161)
6x+21y= 483_________4
Subtracting equation 3 and 4
6x+10y=274
6x+21y=483
-     -         -
       11y = 209

insa · Answer

y= 209/11
y=19
3x+5(19)= 137
3x=137-95
3x=42
x=42/3
x=14
So, solution are= dvds=y=$19
                               cds=x=$14

insa · Answer

check= 2x+7y=161
2(14)+7(19)= 161
28+133=161
161=161