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 three-point questions and 14 five-point questions.

Explanation:

We can substitute a definition of one of the variables by rearranging the first equation.

We set the first equation equal to one of our two variables.

`y = 24 - x`

Now we substitute this equality into our second equation

`3x + 5(24 - x) = 100`