Question

Joe bought two new compact discs and three used compact discs for $54 at the same prices Susan bought three new compact discs and one used compact discs for $53 find the cost of buying a new and used compact disc

Answer 1

Joe:

2 new compact discs

3 used compact discs

total cost : $54

x = price of a new compact disc

y= price of a used compact disc

2x+3y= 54 (a)

Susan :

3 new compact discs

1 used compact disc

total cost : $53

3x+y= 53 (b)

We have the system of equations:

2x+3y= 54 (a)

3x+y= 53 (b)

Multiply (b) by 3 and subtract (a) to (b)

9x+3y= 159

-

2x+3y= 54

__________

7x = 105

Solve for x

x=105/7

x= 15

Replace x on any equation and solve for y:

3x+y= 53 (b)

3(15)+y= 53

45+y= 53

y=53-45

y= 8

Cost of a new compact disc: $15

Cost of a used compact disc = $8