Question

Grant noticed that there were three different types of questions on a test: True/False,

free response, and Multiple Choice. His test had a total of 28 questions. His teacher
told him T/F questions were worth 2 pts. FRQ were worth 5 pts, and MC were worth
4 pts for a total of 100 pts on the test. He also knows that the number of MC
questions on the test is 2 more than the number of FRQ's. How many FRQ's will be
on the test?

Answer 1

To find the number of free response questions on the test, we can set up an equation using the given information. Using substitution, elimination, or graphing, we can find the value of FRQ.

Step-by-step explanation:

Let's assume the number of True/False questions on the test is T, the number of free response questions is FRQ, and the number of Multiple Choice questions is MC.

According to the given information, we know that T + FRQ + MC = 28 (the total number of questions on the test). We also know that the number of MC questions is 2 more than the number of FRQ questions, so we can write the equation MC = FRQ + 2.

Since True/False questions are worth 2 points each, free response questions are worth 5 points each, and Multiple Choice questions are worth 4 points each, we can set up the equation 2T + 5FRQ + 4MC = 100 (the total number of points on the test).

Now we can substitute MC = FRQ + 2 into the equation to solve for FRQ:

2T + 5FRQ + 4(FRQ + 2) = 100

2T + 5FRQ + 4FRQ + 8 = 100

2T + 9FRQ + 8 = 100

2T + 9FRQ = 92

We can solve this equation using substitution, elimination, or graphing to find the value of FRQ. The value of FRQ represents the number of free response questions on the test.