A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 points. How many 4-point problems are there?

Question

A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 points. How many 4-point problems are there?

Answer 1

Here's what we know:

a + b = 30 (there are 30 points to the test)

3a + 4b = 100 (the three and four-point questions add up to 100)

 

Let's use elimination to solve this. Multiply the first equation by -3:

-3a - 3b = -90

3a + 4b = 100

--------------------

b = 10

 

Now that we know b, we can solve for a:

a + 10 = 30

Subtract 10 from both sides:

a = 20

 

Check:

3 * 20 + 4 * 10 = 100

60 + 40 = 100

100 = 100

So 20 three-point and 10 four-point questions