# Question #3686f

##### 1 Answer

#### Explanation:

The best thing to do when dealing with hard and annoying math problems is take away the fluff and identify all the important info:

- 60 points total
- 15 questions total
- Multiple choice questions are two points each
- Open-ended are five points each

So, what don't we know? We don't know how many open-ended and multiple choice questions there are, and that's what we're trying to find. And what do we do when we don't know something? Assign it a variable! We'll have the number of open-ended questions be

Because there are only two types of questions and 15 questions total, we know that the number of open-ended questions plus the number of multiple choice questions is 15:

And we also know that there are 60 points total. If multiple-choice questions are two points each, that means the total number of points for answering multiple choice questions correctly is

Let's see. It appears we have the system:

We are being asked for the number of multiple-choice questions, so we have to solve this system for

Now substitute this for

That means there are 5 multiple-choice questions on the test, and