Question

Mr. Martin’s math test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. 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

Answer 1

Answer:

The number of questions worth 5 points is 14 and the number of questions worth 2 points is 15. 70 points can be gained from the 5 point questions and 30 points can be gained from the 2 point questions making a total of 100 points.

Step-by-step explanation:

For this problem, we have to solve for x and y. We are given two equations.

x + y = 29

5x + 2y = 100

Let's find the value of x first. We can rearrange the first equation so it'll be easier to find the value of x using the second equation.

x + y = 29 → y = -x + 29

Now, let's plug in this equation into the second equation.

5x + 2(-x + 29) = 100

Distribute 2 to (-x + 29)

5x - 2x + 58 = 100

Combine like terms.

3x + 58 = 100

Subtract 58 from 100.

3x = 42

Divide by 3 on both sides.

x = 14

So, the value of x is 14.

Now, let's find the value of y. We can do this by plugging in our x into the first equation.

14 + y = 29

Subtract 14 from 29.

y = 15

So, the value of y is 15.