How many CDs did Juan produce?

Question

Can someone help me with this problem? Please show all the steps:

 

Juan's band produced a number of CDs to sell at a gig. The batch of CDs cost $170.00 to make and each CD was sold for $2.50 more than it cost to produce. Juan gave 2 CDs to his friends, but sold the rest for a total of $198.00. How many CDs did Juan produce?

Answer 1

 

x=# of CDs produced

y=cost to produce each CD

y+$2.50=selling price of each CD

xy=$170

(x-2)(y+$2.50)=$198; Juan gave away 2 CDs leaving (x-2) CDs to sell at $2.50 more to make $198

from xy=170...

y=170/x

substituting

(x-2)[(170/x)+2.5)=198

multiply both sides by x

(x-2)(170+2.5x)=198x

170x-340+2.5x^2-5x=198x

165x-340+2.5x^2=198x

165x-198x-340+2.5x^2=0

-33x-340+2.5x^2=0

multiply both sides by 2

-66x-680+5x^2=0

5x^2-66x-680=0

5*680=3400

34*100=3400

100-34=66

factor

(5x+34)(x-20)=0

x-20=0

x=20 CDs costing $170/20=$8.50 each to make

18 CDs left after giving away 2

each CD was sold for $8.50+$2.50=$11

18*$11=$198

20 CDs were produced