A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.

Question

Each black-and-white copy costs $0.15
Each color copy costs $0.25.

Which system of equations can be used to find b, the number of black-and-white copies, and c, the number of color copies that the customer paid for at the print shop?
A.b + c = 8.00
0.15b + 0.25c = 68
B.b + c = 68
0.15c + 0.25b = 6.00
C.b + c = 6.00
0.25b + 0.15c = 68
D.b + c = 68
0.15b + 0.25c = 6.00

Answer 1

To formulate the correct system of equations, let's define the variables:

• Let \( b \) be the number of black-and-white copies.
• Let \( c \) be the number of color copies.

From the problem, we know two key pieces of information:

1. The total number of copies (black-and-white and color) is 68.
2. The total cost of the copies is $6.00, with black-and-white copies costing $0.15 each and color copies costing $0.25 each.

We can create the following equations based on this information:

1. The equation reflecting the total number of copies: \[ b + c = 68 \]

2. The equation reflecting the total cost of the copies: \[ 0.15b + 0.25c = 6.00 \]

Therefore, the system of equations is: \[ b + c = 68 \] \[ 0.15b + 0.25c = 6.00 \]

Looking at the provided options:

• Option A: \( b + c = 8.00 \) (incorrect)
• Option B: \( b + c = 68 \) and \( 0.15c + 0.25b = 6.00 \) (incorrect)
• Option C: \( b + c = 6.00 \) (incorrect)
• Option D: \( b + c = 68 \) and \( 0.15b + 0.25c = 6.00 \) (correct)

Thus, the correct answer is D.