Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

Answer 1

We can solve this system using elimination:

(x+y=24)3
3x+5y=100

3x+3y=72
-(3x+5y=100)
0x-2y=-28
y=14

We can then plug this back into one of the original equations:

x+14=24
x=10

We can check our answer by plugging this into both of the original equations:

10+14=24
24=24

3(10) + 5(14)=100
30+70=100
100=100

Therefore, there are 10 3-point questions and 14 5-point questions.