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? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

Answer 1

The answer to your question is B :)

Answer 2

We must solve the system in order to find an answer.
Let's solve the system of equations:

`x + y = 24\\ 3x + 5y = 100`
Now let us multiply the first equation by -3:

`x + y = 24/\cdot(-3)\\ 3x + 5y = 100\\ --------\\ -3x-3y=-72\\ 3x + 5y = 100`
We add those two equations together( 3x-3x will cancel out):

`-3x-3y=-72\\+ 3x + 5y = 100\\ --------(+)\\ 2y=28\\ y=14`
Now we simply plug y=14 into any of the starting equations to find x:

`x + y = 24\\ x+14=24\\ x=10`
The answer is B:
The test contains 10 three-point questions and 14 five-point questions.