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notka56 [123]
3 years ago
7

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?
Mathematics
1 answer:
natka813 [3]3 years ago
6 0

Answer:

Cost of 1 DVD is $6.5

Cost of one CD is $4.5

Combine cost of one DVD and CD is $11

Step-by-step 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(\frac{22-2y}{2} )+y=20

33-3y+y=20

33-2y=20

33-20=2y

13=2y

\frac{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=\frac{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


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