Question

A test has twenty questions worth 100 points. The text consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many questions of each type are on the test?

Answer 1

5 Multiple Choice Questions

15 True/False Questions

Checking:

(5 · 11) + (15 · 3) = 100

55 + 45 = 100

Explanation:

t = True/False Questions

m = Multiple Choice Questions

t + m = 20

3t + 11m = 100

To solve this problem, we need to eliminate one of our variables. Looking at the two equations, it seems that the variable t would be easier to eliminate if we multiply the first equation by -3.

t + m = 20

( t + m = 20 ) -3

-3t + ( -3m) = -60

Now we can use the elimination method by adding the two equations together, eliminating the variable t in the process.

-3t + ( -3m) = -60

+ 3t + 11m = 100

8m = 40

m = 5

~Hope this helps!~