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 :
⇒[tex]3x+y=20[/tex] ---(a)
Joel bought 2 used CDs and 2 used DVDs. she spent $22.
So, equation becomes:
⇒[tex]2x+2y=22[/tex] --(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)
[tex]3(\frac{22-2y}{2} )+y=20[/tex]
[tex]33-3y+y=20[/tex]
[tex]33-2y=20[/tex]
[tex]33-20=2y[/tex]
[tex]13=2y[/tex]
[tex]\frac{13}{2} =y[/tex]
[tex]6.5 =y[/tex]
Thus cost of 1 DVD is $6.5
Now substitute this value of y in b to get value of x
⇒[tex]2x+2(6.5)=22[/tex]
⇒[tex]2x+13=22[/tex]
⇒[tex]2x=22-13[/tex]
⇒[tex]2x=9[/tex]
⇒[tex]x=\frac{9}{2}[/tex]
⇒[tex]x=4.5[/tex]
Thus the cost of one CD is $4.5
Hence the combine cost of one DVD and CD = $6.5+ $4.5=$11
