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

the test contains 10 3-point questions and 14 5-point questions.

Explanation:

Answer 2

x=number of 3 point questions
y=number of 5 point questions
The total number of questions was 24.

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

Multiply the first equation by negative 3:
-3x-3y=-72
3x+5y=100
Add the equations together:
2y=28
y=14

Plug 14 for y into the first original equation:
x+y=24
x+14=24
x=10

This indicates that the test contained 10 3-point questions and 14 5-point questions.