John bought 9 CDs. Some of them cost $12.75, and the rest cost $11.95. The total was $112.35. How many did he buy at each price?
a + b = 9 ... 11.95 a + 11.95 b = 107.55
12.75 a + 11.95 b = 112.35
subtracting equations (to eliminate b) ... .80 a = 4.80
solve for a , then substitute back to find b
Step 1: Let's assume the number of CDs that John bought at $12.75 each is x.
Step 2: So, the number of CDs that John bought at $11.95 each is 9 - x (since he bought a total of 9 CDs).
Step 3: The cost of x CDs at $12.75 each is 12.75 * x.
Step 4: The cost of (9 - x) CDs at $11.95 each is 11.95 * (9 - x).
Step 5: According to the problem, the total cost was $112.35.
Step 6: Putting it all together, we have the equation: 12.75x + 11.95(9 - x) = 112.35.
Step 7: Simplifying the equation, we get: 12.75x + 107.55 - 11.95x = 112.35.
Step 8: Combining like terms, we have: 0.8x + 107.55 = 112.35.
Step 9: Subtracting 107.55 from both sides, we get: 0.8x = 4.8.
Step 10: Dividing both sides by 0.8, we get: x = 6.
Step 11: Therefore, John bought 6 CDs at $12.75 each and 9 - 6 = 3 CDs at $11.95 each.
To solve this problem, let's assume that John bought x CDs at the price of $12.75 and (9 - x) CDs at the price of $11.95.
So, the cost of x CDs at $12.75 each would be 12.75x, and the cost of (9 - x) CDs at $11.95 each would be 11.95(9 - x).
We also know that the total cost of all the CDs was $112.35. Therefore, we can set up the equation:
12.75x + 11.95(9 - x) = 112.35
Expanding the equation, we get:
12.75x + 107.55 - 11.95x = 112.35
Combining like terms, we have:
(12.75 - 11.95)x + 107.55 = 112.35
0.80x + 107.55 = 112.35
Subtracting 107.55 from both sides of the equation, we get:
0.80x = 4.80
Dividing both sides by 0.80, we find:
x = 6
So, John bought 6 CDs at $12.75 each and (9 - 6) = 3 CDs at $11.95 each.
Therefore, he bought 6 CDs at $12.75 and 3 CDs at $11.95.