Question

Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Write the system of equations that could be used to solve for the number of pens, p, and the number of markers, m, bought.

p + m = _____

Answer 1

___p + _______m =_______

Answer 2

To set up the system of equations, we can establish two equations based on the information provided.

1. The first equation is based on the total number of pens and markers:
\[
p + m = 19
\]

2. The second equation is based on the total cost of the pens and markers:
\[
0.25p + 0.75m = 11.50
\]

So, the complete system of equations is:

\[
\begin{align*}
1. & \quad p + m = 19 \\
2. & \quad 0.25p + 0.75m = 11.50
\end{align*}
\]

Answer 3

To express the equations in the requested format with blanks filled in, we can rewrite both equations:

1. For the number of pens and markers:
\[
1p + 1m = 19
\]

So, it can be filled in as:
\- **1**p + **1**m = **19**

2. For the total cost of pens and markers, we can eliminate the decimals by multiplying the entire equation by 100:
\[
25p + 75m = 1150
\]

So, it can be filled in as:
\- **25**p + **75**m = **1150**

Thus, your response would be:
- For the first equation: **1**p + **1**m = **19**
- For the second equation: **25**p + **75**m = **1150**