SOLUTION: 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 cos

Question 276428: 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 the used CD and the used DVD
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
C = number of CDs
D = number of DVDs
.
Kate bought 3 CDs and 1 DVDs for $20:
3C + D = 20
.
Joel bought 2 CDs and 2 DVDs for $22:
2C + 2D = 22
.
Two equations and two unknowns can be solved using simultaneous equations.
.
3C + D = 20
2C + 2D = 22
.
Multiply the first equation by 2 and then subtract the second equation:
6C + 2D = 40
2C + 2D = 22
4C = 18
C = 4.50
.
Substituting to find D:
2C + 2D = 22
2(4.5) + 2D = 22
2D = 13
D = 6.50
.
Checking
3C + D = 20 ??
3(4.50) + 6.50 = 13.50 + 6.50 = 20
Yes.
.
Double checking...
2C + 2D = 22 ??
2(4.50) + 2(6.50) = 9 + 13 = 22
Yes.
.
Answer:
Used CDs cost $4.50 and used DVDs cost $6.50.
.
Done.
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