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

Solve the two equations simultaneously:
3x+5y=100
x+y=24
Multiply the 2nd equation by 3 so you can have the same coefficient of one of the variables (in this case, x)
3x+5y=100
3x+3y=72
Minus the second equation from the first to give you:
2y=28
Divide by 2 on both sides to give you y=14
Substitute 14 for y into one of the equations:
x+y=24
x=10
Remember that 3x+5y=100
So the test contains 10 3 point questions and 14 5 point questions.