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

Remark. The easiest way to solve this is to make the coefficients of one of the letters = to the same coefficient in the other equation

Set up and solve
x + y = 24
3x + 5y = 100   Multiply the first equation by 3
3x + 3y =   72   Subtract
2y =           28   Divide by 2
y   =           28/2
y   =           14  <<<<<<  Answer for y

Step 2
Solve for x
x + y = 24
x + 14 = 24    Subtract 14 from both sides.
x = 24 - 14
x = 10  <<<<Answer for x

Check to see if it works.

3x + 5y = 100
3*10 + 5*14 = 100
30 + 70 = 100        Checks.

There are 10 three point  question
There are  14 five point questions.