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

Rewrite x+y = 24 as x = 24-y

Replace x in the 2nd equation with the rewritten equation:

3(24-y) + 5y = 100

Distribute the 3:

72-3y +5y = 100

Combine like terms:

72 +2y = 100

Subtract 72 from each side:

2y = 28

Divide both sides by 2:

y = 14

To fid X replace y with 24 in the first equation:

x + 14 = 24

X = 10

There are 10 3 point questions and 14 5 point questions.