Solving Systems of Linear Equations: Graphing — Unit test
Question 10 • Algebra III A
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 = 243x + 5y = 100What 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 10 three-point questions and 14 five-point questions.
C
The test contains 14 three-point questions and 10 five-point questions.
D
The test contains 20 three-point questions and 8 five-point questions.
Explanation
The first equation says there are 24 questions total. Multiply it by 3 to get 3x + 3y = 72, then subtract this from 3x + 5y = 100; this gives 2y = 28, so y = 14. Then x = 24 − 14 = 10, meaning the test has 10 three-point questions and 14 five-point questions.
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