A Math Test Is Worth 100 Points and Has 38 Problems. Each Problem Is Worth Either 5 Points or 2 Poin

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations:

1. m + t = 38
2. 5m + 2t = 100

Rearrange (1) to solve for m - subtract t from each side:
3. m = 38 - t

Now, substitute (3) into (2)
5(38 - t) + 2t = 100
190 - 5t + 2t = 100

Combine like terms:
190 - 3t = 100

Using our equation solver, we get t = 30.

Plugging t = 30 into (1), we get:
30 + t = 38

Using our equation solver again, we get m = 8.

Check our work for (1)
8 + 30 = 38 <-- Check

Check our work for (2)
5(8) + 2(30) ? 100
40 + 60 ? 100
100 = 100 <-- Check

You could also use our simultaneous equations calculator