# Barb wants to get 8 out of every 10 questions right on her test. If there are 35 questions on the test, how many Barb want to get right?

Jan 12, 2017

She will want to get $28$ questions right out of $35$.

#### Explanation:

Barb wants to get a certain proportion of the questions right. That proportion is "8 right for every 10 answered". This can be written as the ratio (or fraction) $\frac{8}{10}$. As long as the ratio remains the same, we can scale these two numbers to whatever values we want, and their proportion won't change. (Well, okay, we scale one of them, and the other will "tag along" to keep the proportion constant.)

Let $x$ be the number of questions Barb needs to get right.

Since there are 35 questions on the test, we seek a ratio equal to $\text{8 right"/"10 total}$ in the form of (x " right")/"35  total". We can now make an equation that sets these two ratios equal to each other, so we can solve for $x$:

$\frac{8}{10} = \frac{x}{35}$

Cross-multiply:

$8 \times 35 = 10 \times x$
$\text{ } 280 = 10 x$

Divide both sides by 10:

$\text{ } 28 = x$

And there it is—the number of questions Barb needs to get right is $28$.

We can check this: $8 \div 10 = 0.8$, and $28 \div 35 = 0.8$ as well. Since the two ratios have the same value, they are equal, and our solution of $x = 28$ is correct.