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?

Question

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 \( y \).