Question

There are 57 students in the class. The ratio of boys to girls is 4:15. How many boys need to leave the room so the ratio becomes 4:11?

Answer 1

We need `48/11` more boys.

Alternatively, `12` girls need to leave the room.

Explanation:

`57 = b + g`

`b/g = 4/15 => g = (15b)/4`

`57 = b + (15b)/4`

`228 = 4b + 15b`

`228/19 = b = 12 => g= 57 - 12 = 45`

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`frac{x}{45} = 4/11`

`11x = 180`

`x = 180/11 = 16.36` boys

`12/y = 4/11`

`132 = 4y`

`y = 33` girls

Answer 2

It would seem that there is a problem with the question....?

If a number of girls would be required to leave it would be `12`

Explanation:

With `57` students in the class we have:

Boys: `4/19 xx 57 =12`

Girls: `15/19 xx 57 = 45`

If boys are asked to leave the room then the number of girls will stay the same.

We would like the scenario of:

`4:11 = x:45`

This will not work with an exact number because `45` is not a multiple of `11` and we will need more boys than there are at present.

`4/11 = x/45`

The required number of boys is:

`x = 16 4/11`

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However, if the question was meant as "How many girls must leave the room?" it would mean that the number of Boys would stay the same and we would have...

`4:11 = 12:x`

`4/11 = 12/x`

`x = (11xx12)/4`

`x= 33` girls

In this case `45-33 = 12` girls would have to leave the room.