Question

Doug got 8 out of 10 questions correct on a math quiz. If each question was worth the same number of points, and the test was worth 50 points total, what was Doug's score?

Answer 1

To solve for this, we need to set up fractional proportions.
We have 8 out of 10, or 8/10, questions correct on the quiz. We have 50 total points, and we're looking for how many points Doug scored.
Since we have 50 total and are looking for a number out of 50, put x/50, x being Doug's score.

Now our fractional proportions are:

8/10 = x/50

To solve for x, we need to cross-multiply the fractions. If you don't quite understand that, multiply the bottom number (denominator) of one fraction by the top number (numerator) of the other fraction.
We will multiply 8, the numerator of 8/10, by 50, the denominator of x/50.

It should look like this:
8 x 50.
Multiply 8 by 50.
8 x 50 = 400.

Now that we have one product down, we need to solve for the other.
Now all we have left to multiply is 10 and x
It should look like this:

10x.

Set your products up as an equation.

10x = 400.

Now, we can solve for x.
Since x is being multiplied by 10, we must divide 10x by 10.
Remember, what you do to one side of an equation (unless it's distributing) you must do to the other.
Divide 400 by 10.

10x / 10 = x
400 / 10 = 40.

You are left with:

x = 40.

I hope this helps!