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?

2 Answers
Vinícius Ferraz
Aug 6, 2018

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#

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

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

#11x = 180#

#x = 180/11 = 16.36# boys

#12/y = 4/11#

#132 = 4y#

#y = 33# girls

EZ as pi
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: #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#

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

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.

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