SOLUTION: In the Independent Practice on pg 93, I am having difficulty setting up the equation for problem 2. Jerome bought 12cds. Some cost 7.50 ea. the rest cost 6.50 each. How many C

Question 162761: In the Independent Practice on pg 93, I am having difficulty setting up the equation for problem 2.
Jerome bought 12cds. Some cost 7.50 ea. the rest cost 6.50 each. How many CDs were bought at each price if he spent $82?
Answer by orca(409) (Show Source): You can put this solution on YOUR website!
Let x be the number of cds that cost $7.5 each.
Let y be the number of cds that cost $6.5 each.
The money spent on the $7.5 cds is 7.5x
The money spent on the $6.5 cds is 6.5y.
Now use the following relationships to set up a system of two equations:
(1) the total number of cds = 12
(2) the total money spent = 82
So
x + y = 12 ..............(1)
7.5x + 6.5y = 82 ...........(2)
Solving equation (1) for y, we have
y = 12 - x ...............(3)
Substituting y = 12 - x into equation (2), we have
7.5x + 6.5(12 - x) = 82
Solving for x, we obtain:
7.5x + 78 - 6.5x = 82
x + 78 = 82
x = 4
Substituting x = 4 into equation (3) to find y, we get
y = 12 - x = 12 - 4 = 8
So Jerome bought 4 $7.5 cds, 8 $6.5 cds.

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