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.

Question

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.