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

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

Explanation:

Let us first find the solution to the system of equations.

x+y= 24

3x+5y= 100

We use substitution method.

x=24-y

Replacing the value of x in the second equation.

3(24-y)+5y=100

Then solve for y.

72-3y+5y=100

2y=100-72

2y=28

y=14

To find x let us replace the value of y in x=24-y

x=24-14

x=10

This means that the test has 14 five-point questions and 10 three point questions.