Question

On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions are on the test?
4
8
12
16

Answer 1

Let x = number of 2-point, y = number of 4-point, z = number of 5-point questions. Then
x + y + z = 28,
2x + 4y + 5z = 100,
x = 2z.

Substitute x = 2z into the first: 2z + y + z = 28 → y = 28 − 3z.
Substitute into the points: 2(2z) + 4(28 − 3z) + 5z = 100 → 112 − 3z = 100 → z = 4.
Thus x = 2z = 8.

Answer: 8