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 10 three-point questions and 14 five-point questions.

The test contains 4 three-point questions and 20 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 three-point questions and 14 five-point questions.

Explanation:

Answer 2

The test contains 10 three-point questions and 14 five-point questions.

Explanation:

Im using substitution.

`x+y=24\\y=24-x\\3x+5(24-x) =100\\3x+120-5x=100\\120-2x=100\\120-120-2x=100-120\\-2x=-20\\(-2x)/(-2) = (-20)/(-2) \\x=10`

This means since x is 3 point questions, there are 10 3-point questions.

`x+y=24\\10+y=24\\10-10+y=24-10\\y=14`

This means since y is 5 point questions, there are 14 5-point questions.