I can purchase 3 cassettes for the price of 2 CD’s. If I buy 3 CD’s and 6 cassettes for $84, then the price of one CD is?

Question

Question:

I can purchase 3 cassettes for the price of 2 CD’s. If I buy 3 CD’s and 6 cassettes for $84, then the price of one CD is?

 

A) $10

B) $11

C) $12

D) $13

Answer 1

 

 X is cost of cassette

 Y is cost of CD

 

3X = 2Y 

 

3X + 6y = 84

 

2y + 6y = 84 <--- substitutes 3x with 2y per the first equation

 

8y = 84 <--- combines like terms

 

y = 84/8 = 42/4  = 21/2 = $10.50

 

3X = 2Y = 2(10.50) = 21

 

X = 21/3 = $7

 

cassette costs $7 and the CD costs $10.50

 

Check:

3 x 7 + 6 x 10.50 = 21 + 63 = 84