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 plus y is equal to 24 3 x plus 5 y is equal to 100 What does the solution of this system indicate about the questions on the test?
Answer
A
The test contains 4 three-point questions and 20 five-point questions.
B
The test contains 14 three-point questions and 10 five-point questions.
C
The test contains 10 three-point questions and 14 five-point questions.
D
The test contains 20 three-point questions and 8 five-point questions.
Explanation
The equations say there are 24 questions total and their point values add to 100. Substitute x = 24 − y into 3x + 5y = 100: 3(24 − y) + 5y = 100, so 72 + 2y = 100 and y = 14. Then x = 24 − 14 = 10, so the test has 10 three-point questions and 14 five-point questions. That is choice C, not B.
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