Question

Kate bought 3 used CDs and 1 used DVD at the bookstore. Her friend Joel bought 2 used CDs and 2 used DVDs at the same store. If Kate spent $20 and Joel spent $22, determine the cost of a used CD and a used DVD?

Answer 1

Cost of 1 DVD is $6.5

Cost of one CD is $4.5

Combine cost of one DVD and CD is $11

Explanation:

Given :

Kate bought 3 used CDs and 1 used DVD at the bookstore.

Her friend Joel bought 2 used CDs and 2 used DVDs at the same store.

Kate spent $20

Joel spent $22

To Find : the cost of a used CD and a used DVD

Solution :

Let cost of 1 used CDs be $x

Let cost of 1 used DVDs be $y

Cost of 3 used CDs = $3x

Cost of 2 used CDs = $2x

Cost of 2 used DVDs = $2y

Kate bought 3 used CDs and 1 used DVD at the bookstore.

She spent $20

So, equation becomes :

⇒
`3x+y=20` ---(a)

Joel bought 2 used CDs and 2 used DVDs. she spent $22.

So, equation becomes:

⇒
`2x+2y=22` --(b)

Now solve (a) and (b) to determine the value of x and y

We will use substitution method

Substitute the value of x from (b) in (a)

`3((22-2y)/(2) )+y=20`

`33-3y+y=20`

`33-2y=20`

`33-20=2y`

`13=2y`

`(13)/(2) =y`

`6.5 =y`

Thus cost of 1 DVD is $6.5

Now substitute this value of y in b to get value of x

⇒
`2x+2(6.5)=22`

⇒
`2x+13=22`

⇒
`2x=22-13`

⇒
`2x=9`

⇒
`x=(9)/(2)`

⇒
`x=4.5`

Thus the cost of one CD is $4.5

Hence the combine cost of one DVD and CD = $6.5+ $4.5=$11