# 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?

We need $\frac{48}{11}$ more boys.

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

#### Explanation:

$57 = b + g$

$\frac{b}{g} = \frac{4}{15} \implies g = \frac{15 b}{4}$

$57 = b + \frac{15 b}{4}$

$228 = 4 b + 15 b$

$\frac{228}{19} = b = 12 \implies g = 57 - 12 = 45$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\frac{x}{45} = \frac{4}{11}$

$11 x = 180$

$x = \frac{180}{11} = 16.36$ boys

$\frac{12}{y} = \frac{4}{11}$

$132 = 4 y$

$y = 33$ girls

Aug 6, 2018

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: $\frac{4}{19} \times 57 = 12$

Girls: $\frac{15}{19} \times 57 = 45$

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.

$\frac{4}{11} = \frac{x}{45}$

The required number of boys is:

$x = 16 \frac{4}{11}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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...

$4 : 11 = 12 : x$

$\frac{4}{11} = \frac{12}{x}$

$x = \frac{11 \times 12}{4}$

$x = 33$ girls

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