Question

A 40 question test has 132 possible points there are M 5 point questions. And N 1 point questions how many of each type of questions is on the test?

Answer 1

There are 23 5-point questions and 17 1-point questions.

Explanation:

there are M 5 point questions

And N 1 point questions

M + N = 40

A 40 question test has 132 possible points

5M + N = 132

We have a system of equations.

M + N = 40

5M + N = 132

Multiply both sides of the first equation by -1. Write the second equation below it. Add the equations.

-M - N = -40

+ 5M + N = 132

----------------------------

4M = 92

M = 23

Now substitute 23 for M in the first equation and solve for N.

M + N = 40

23 + N = 40

N = 17

There are 23 5-point questions and 17 1-point questions.

Answer 2

Answer:the number of 5 point questions is 23

the number of 1 point questions is 17

Explanation:

Let M represent the number of 5 point questions.

Let N represent the number of 1 point questions.

The total number of questions in the test is 40. It means that

M + N = 40 - - - - - - - - - - - - 1

The possible total points in the test is 132 and it contains M 5 point questions and N 1 point questions. This means that

5M + N = 132 - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

- 4M = - 92

M = - 92/-4 = 23

Substituting M = 23 into equation 1, it becomes

23 + N = 40

N = 40 - 23 = 17