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.
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Answer 1

Answer: B) 10 three-point questions and 14 five-point questions

Explanation:

x represents three-point questions

y represents five-point questions

3x + 5y = 100 → 1(3x + 5y = 100) = 3x + 5y = 100

x + y = 24 → -3(x + y = 24) = -3x -3y = -72

2y = 28

y = 14 (five-point questions)

x + y = 24

x + 14 = 24

x = 10 (three-point questions)