Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 poir

points. If x is the number of 3-point questions and y is the number of 5-point questions, the system sho
represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
O The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
O The test contains 14 three-point questions and 10 five-point questions.
O The test contains 20 three-point questions and 8 five-point questions.

Answer 1

The test contains 10 three-point questions and 14 five-point questions.

Explanation:

3x + 5y = 100, so:

x - number of 3-point questions

y - number of 5-point questions

x + y = 24 ⇒ y = 24 - x

3x + 5y = 100

3x + 5(24-x) = 100

3x + 120 - 5x = 100

-2x = -20

x = 10

y = 24 - 10 = 14