Your math test has 38 questions and is worth 200 points. The test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. How many of each type of question are there?

2 Answers
Mar 29, 2018

3 open ended questions
35 multiple choice questions

Explanation:

We will give multiple-choice questions the variable x and open-ended questions the variable y.

Since there are 38 questions total we know that:
x + y = 38

We also know that the multiple choice are worth "4 points" and the open-ended questions are worth "20 points". The total number of available points is 200 points, so here is our second equation:
4x + 20y = 200

Now we can rearrange the first equation so that we are able to substitute it into the second equation:
x + y = 38
x = 38 - y

Now substitute and solve:

4x + 20y = 200

4(38 - y) + 20y = 200

152 - 4y + 20y = 200

152 + 16y = 200

16y = 48

y = 3

There are 3 open-ended questions.

Now substitute in 3 and solve for x:

x = 38 - y

x = 38 - (3)

x = 35

There are 35 multiple choice questions.

Mar 29, 2018

There are 35 multiple choice questions and 3 open-ended questions.

Explanation:

Let x be the number of multiple choice questions and let y be the number of open-ended questions.
x+y = 38
4x + 20y = 200

Multiplying the first equation by 4:
4x + 4y = 152

Subtracting the second equation from the first equation:
16y = 48
y = 48/16
y = 3

Plugging in 3 for y in the first equation:
x + 3 = 38
x = 38-3
x = 35