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?
O The test contains 4 three-point questions and 20 five-point questions.
O 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 solution of the system indicates that the test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

The given system of equations represents the number of 3-point and 5-point questions on the science test. Let's solve the system to find the values of x and y. From the first equation, we have x + y = 24. Rearranging the equation, we can solve for x by subtracting y from both sides: x = 24 - y. Substituting this value of x into the second equation, we get 3(24-y) + 5y = 100. Expanding and simplifying, we get 72 - 3y + 5y = 100. Combining like terms, we get 2y = 28, and solving for y, we find that y = 14. Substituting this value of y back into the first equation, we find x = 10.

Therefore, the solution of the system indicates that the test contains 10 three-point questions and 14 five-point questions.

Learn more about Solving a system of equations for the number of 3-point and 5-point questions on a test