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.

What is the equation for x and y?

Answer 1

To set up a system of equations based on the information provided, we can create two equations corresponding to the total number of problems and the total points.

1. Total Problems Equation: \[ x + y = 35 \] Here, \(x\) is the number of 5-point questions, and \(y\) is the number of 2-point questions. Together, they must total 35 problems.

2. Total Points Equation: \[ 5x + 2y = 100 \] In this equation, \(5x\) represents the total points from the 5-point questions, and \(2y\) represents the total points from the 2-point questions. Together, they must total 100 points.

Thus, the system of equations is: \[ \begin{cases} x + y = 35 \ 5x + 2y = 100 \end{cases} \]