Question 5157: Leanna has $37 to spend in a record store. She can spend all of the money on two compact discs and a cassette, or she can buy one CD and two cassettes and have $5 left over. What is the price of a CD? What is the price a cassette?
Answer by Abbey(339)   (Show Source):
You can put this solution on YOUR website! Let x = CD
Let y = Cassette
We know that 37dollars will purchase 2 CDs and a cassette, so:
37=2X+y
Also, 37 dollars will buy one CD and 2 cassettes and 5 will be left over, so:
37=x+2Y+5
Set these two equations equal to one another, because they both total $37
2x+y=x+2y+5
Solve for x by subtracting x-y from both sides:
x=y+5
Use one of your equations to figure out what y=
37=2x+y
37=2(y+5)+5
37=2y+10+5
37=2y+15
subtract 15 from both sides:
18=2y
divide both sides by 2
9=y
now put the y value into an equation and find out what x is:
x=y+5
x=9+5
x=14
So a CD costs $14 and a cassette costs $9.
Check your answers with the problem to verify.
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