Best Buy was having a special in all their tapes and CDs. Jane was able to buy 4 tapes and 3 CDs for $54. Larry bought 6 CDs and 3 tapes for $78. How much did a CD cost on special?

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Answer 1 · 2018-05-30T14:57:41

#$10 # per CD, #$6# per tape

Tapes?

#4t+3c=54#

#6c+3t=78#

#8t+6c=108#

#8t - 3t = 108-78 #

#5t = 30#

#t = 6#

#c = 1/3 (54-4t)=1/3(54-24)=10 #

#$10 # per CD, #$6# per tape

Answer 2 · 2018-05-30T15:23:47

Tapes are $6 and CDs are $10.

t=tapes
c = CDs

#4t+3c = 54#
#3t+6c=78#

Two linear equations with two unknowns:

#-2(4t+3c = 54)#
#3t+6c=78#

#-8t-6c = -108#
#3t+6c=78#

add them up:

#-5t = -30#

#t=6#

use either of the original equations to solve for c:

#4t+3c = 54#

#4(6)+3c = 54#

#24+3c = 54#

#3c = 30#

#c=10#

So tapes are $6 and CDs are $10.