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:
- = the number of black-and-white copies.
- = the number of color copies.
1. The total number of copies is 68:
This gives us the equation:
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:
Thus, the two correct equations representing the system are:
These two equations can be solved to find and .
Do you want the detailed steps to solve this system? Here are some questions to explore further:
- How do you solve a system of linear equations using substitution?
- How do you solve a system of linear equations using elimination?
- What happens if the total number of copies changes but the prices remain the same?
- How does the solution change if black-and-white copies are cheaper?
- 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
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