Question

Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test.

Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.

x + y = 29, 5x + 2y = 100
x + y = 100, 5x + 2y = 29
5x + y = 29, 2y + x = 100
2x + y = 100, 5y + x = 29

Answer 1

To create a system of equations based on the problem description, we define variables as follows:

- Let \( x \) be the number of problems worth 5 points each.
- Let \( y \) be the number of problems worth 2 points each.

The problem provides us with two key pieces of information:

1. The total number of problems is 29.
2. The total number of points for the test is 100.

These statements can be translated into equations:

1. The first equation represents the total number of problems:
\[
x + y = 29
\]

2. The second equation represents the total points scored:
\[
5x + 2y = 100
\]

Thus, the correct system of equations to describe the situation is:
\[
\begin{align*}
x + y &= 29 \\
5x + 2y &= 100
\end{align*}
\]

Therefore, the correct option is:
- **x + y = 29, 5x + 2y = 100**.