Question

Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 35 problems. Each problem is worth either 5 points or 2 points. How can you set up a system of equations to find how many problems of each point value are on the test?

Let x = the number of questions worth 5 points.

Let y = the number of questions worth 2 points.

Answer 1

To set up a system of equations for the problem, we need to incorporate the information given about the total number of problems and the total point value.

We have two variables defined:
- Let \( x \) = the number of problems worth 5 points.
- Let \( y \) = the number of problems worth 2 points.

From the problem, we know the following:

1. The total number of problems is 35.
2. The total point value of the test is 100 points.

Using this information, we can set up the following equations:

1. **For the total number of problems:**
\[
x + y = 35
\]

2. **For the total point value:**
\[
5x + 2y = 100
\]

Now we have a system of equations:

\[
\begin{align*}
1. & \quad x + y = 35 \quad \text{(total problems)} \\
2. & \quad 5x + 2y = 100 \quad \text{(total points)}
\end{align*}
\]

You can now solve this system of equations to find the values of \( x \) and \( y \).