Question

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?

Answer 1

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.

Answer 2

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`