Math Problem Statement

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 cost $0.08. • Each color copy cost $0.15.

Select TWO equations that represent the system of equations that 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.

b + c = 6.00 0.08b + 0.15c = 6.00 0.15b + 0.08c = 68 0.15b + 0.08c = 6.00 0.08b + 0.15c = 68 b + c = 68

Solution

The problem gives us two important pieces of information: the total number of copies and the total cost. We are asked to find two equations that model the situation.

Let's define the variables:

  • bb = the number of black-and-white copies.
  • cc = the number of color copies.

1. The total number of copies is 68:

This gives us the equation: b+c=68b + c = 68

2. The total cost of the copies is $6.00. Each black-and-white copy costs $0.08, and each color copy costs $0.15:

This gives us the equation: 0.08b+0.15c=6.000.08b + 0.15c = 6.00

Thus, the two correct equations representing the system are:

  • b+c=68b + c = 68
  • 0.08b+0.15c=6.000.08b + 0.15c = 6.00

These two equations can be solved to find bb and cc.

Do you want the detailed steps to solve this system? Here are some questions to explore further:

  1. How do you solve a system of linear equations using substitution?
  2. How do you solve a system of linear equations using elimination?
  3. What happens if the total number of copies changes but the prices remain the same?
  4. How does the solution change if black-and-white copies are cheaper?
  5. What if the cost of color copies is increased to $0.20?

Tip: When solving systems of equations, carefully check units and coefficients to ensure the equations correctly represent the situation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations

Formulas

b + c = 68
0.08b + 0.15c = 6.00

Theorems

System of Equations

Suitable Grade Level

Grades 6-8