A customer paid a total of $16 for 74 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 $0.15. Each color copy cost $0.29. 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?

Question

A customer paid a total of $16 for 74 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 $0.15. Each color copy cost $0.29. 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?

Answer 1

b + c = 74 (the total number of copies purchased is the sum of black-and-white and color copies)

0.15b + 0.29c = 16 (the total cost is the sum of the cost of black-and-white copies and the cost of color copies)

Answer 2

Which graph best represents this system of equations and its solution?

`8x-4y=-16`

`3x+15y=-6`

Answer 3

To graph this system of equations, we first need to rewrite them in slope-intercept form (y = mx + b), which means solving for y:

8x - 4y = -16

-4y = -8x - 16

y = 2x + 4

3x + 15y = -6

15y = -3x - 6

y = (-1/5)x - (2/5)

Now we can graph these two lines and find their point of intersection, which is the solution to the system of equations:

![graph](https://www.mathsisfun.com/algebra/images/graph-2-lines.svg)

The solution is the point (-2, 0.4).

Therefore, the correct graph is **(A)**.

Answer 4

Let's denote the number of black-and-white copies as b and the number of color copies as c.

The cost of black-and-white copies can be calculated by multiplying the number of black-and-white copies (b) by the cost of each black-and-white copy ($0.15). Therefore, the total cost of black-and-white copies is 0.15b.

Similarly, the cost of color copies can be calculated by multiplying the number of color copies (c) by the cost of each color copy ($0.29). Therefore, the total cost of color copies is 0.29c.

According to the problem statement, the total cost of all copies is $16. Therefore, the equation can be set up as:

0.15b + 0.29c = 16

This equation represents the total cost equation.

The second equation is a constraint equation based on the number of copies. The customer paid a total of 74 copies, which means the sum of the number of black-and-white copies (b) and the number of color copies (c) is 74:

b + c = 74

These two equations, 0.15b + 0.29c = 16 and b + c = 74, can be used to find the number of black-and-white copies (b) and the number of color copies (c).