Question

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?

Answer 1

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 `-> 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 `-> 4/9` of the whole.

girls `->5/9` of the whole.

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

`4/9xx3321 = 1476`

Answer 2

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:

`color(brown)("Case 1. 'if the total num of students is 3321' ")`

`color(brown)("Case 2. 'if the total num of girls is 3321'")`

My other answer assumes case 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering as if Case 2 is applicable")`

Using ratio in fraction FORMAT.

`color(brown)("Note that this is not fractions of the whole.")`

`("boys")/("girls") -> 4/5-=x/3321`

Multiply both sides by 3321

`x=2656.8`

This `ul("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