# The ratio of boys to girls at a college is 4:5. How many boys and are there if the total num of students is girls 3321?

Jan 10, 2017

boy count is 1476

#### Explanation:

There is an important difference between the way counts are viewed in ratio to that in fractions.

The ratio of boys : girls $\to 4 : 5$ so you have 4 boys and 5 girls making the whole count $4 + 5 = 9$ in its simplest form.

So to change the ratio proportion into fraction proportion we have:

boys $\to \frac{4}{9}$ of the whole.

girls $\to \frac{5}{9}$ of the whole.

It is given that the whole is 3321 therefore the count of boys is:

$\frac{4}{9} \times 3321 = 1476$

Feb 19, 2018

An alternative interpretation of the question.
Proves that my other solution is the correct one.

#### Explanation:

There is a problem with interpreting the question part:
"the total num of students is girls 3321"

It would make more sense if worded:

$\textcolor{b r o w n}{\text{Case 1. 'if the total num of students is 3321' }}$

$\textcolor{b r o w n}{\text{Case 2. 'if the total num of girls is 3321'}}$

My other answer assumes case 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering as if Case 2 is applicable}}$

Using ratio in fraction FORMAT.

$\textcolor{b r o w n}{\text{Note that this is not fractions of the whole.}}$

$\left(\text{boys")/("girls}\right) \to \frac{4}{5} \equiv \frac{x}{3321}$

Multiply both sides by 3321

$x = 2656.8$

This $\underline{\text{answer does not make sense}}$

You can not have part of a boy. So the other solution where I address Case 1 must be the correct interpreatation