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

@lowkey

Answer 2

You remember how I said you have two methods to get to a solution right?
In the substitution method, you use one equation to solve for one variable and then substitute that expression into the other equation to solve for the other variable.
In the elimination method, you make one of the variables cancel itself out by adding the two equations.
Which do you think you should use for this problem?

Answer 3

Either method is okay but one comes easier than the other

Answer 4

which is the easier one

Answer 5

Substitution! Since the first formula has no coefficients on the variables it is very easy to change the formula up a bit and then substitute it into the second equation.
x+y=24
Let's decide to substitute the x variable. Meaning, we are going to make it equal to x so we can plug in the formula into the second equation under the x variable.
Subtract y from both sides, and your ready to substitute equation is x=24-y

Answer 6

wait so is the answer b?

Answer 7

Next we can plug that formula into the second equation.
3x+5y=100
3(24-y)+5y=100 Distribute
72-3y+5y=100 Simplify like terms
2y+72=100
2y=28
y=14

Answer 8

So now we know that y (number of 5 point questions) is 14. So yes, B is correct

Answer 9

ok

Answer 10

But you should double check by finding x as well.

Answer 11

oh ok