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.

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?

Let $ b $ represent the number of black-and-white copies, and $ c $ represent the number of color copies.

We are given the following information:

1. **Total number of copies**: The customer made a total of 68 copies, so:
   \[
   b + c = 68
   \]

2. **Total cost of the copies**: The customer paid a total of $6.00 for these copies. The cost per black-and-white copy is $0.15, and the cost per color copy is $0.25. Therefore, the total cost of the copies can be written as:
   \[
   0.15b + 0.25c = 6.00
   \]

Thus, the system of equations to find $ b $ (black-and-white copies) and $ c $ (color copies) is:

\[
\begin{aligned}
b + c &= 68 \\
0.15b + 0.25c &= 6.00
\end{aligned}
\]

Would you like to solve this system, or do you have any other questions?

### Related Questions:
1. How can this system of equations be solved using substitution?
2. What is the solution to this system using the elimination method?
3. How can you interpret the meaning of the solution in terms of the original problem?
4. How does changing the cost of color copies affect the solution?
5. What if the total number of copies was different—how would the system change?

**Tip**: When solving a system of equations, substitution works best when one equation is easily solved for a single variable, while elimination is useful when you can easily combine terms to cancel out one variable.

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. Each black-and-white copy costs $0.15 and 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?

Learn how to solve a system of linear equations to determine the number of black-and-white and color copies made at a print shop. The problem includes key algebraic concepts, such as forming and solving a system of equations. Suitable for students in Grades 8-10.

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