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?

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.

Answer 1

Answer:

B

Step-by-step explanation:

To solve this system, solve by substitution.

Rewrite x + y = 24 as x = 24 - y. Substitute it into 3x + 5y = 100.

3(24 - y) + 5y = 100

72 - 3y + 5y = 100

2y = 28

y = 14 5-point questions

Substitute y = 14 back into x = 24 - y and solve for x.

x = 24 - 14

x = 10 3-point questions