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.

#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
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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#

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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Answer 3

To find out how many boys need to leave the room so the ratio becomes 4:11, follow these steps:

  1. Determine the initial number of boys and girls: Boys = (4 / (4 + 15)) * 57 Girls = (15 / (4 + 15)) * 57

  2. Calculate the initial number of boys and girls: Boys = (4 / 19) * 57 Girls = (15 / 19) * 57

  3. Calculate the current number of boys: Current number of boys = (4 / 19) * 57

  4. Calculate the current number of girls: Current number of girls = (15 / 19) * 57

  5. Determine the target number of boys: Target number of boys = (4 / (4 + 11)) * (Current number of boys + Current number of girls)

  6. Calculate the target number of boys: Target number of boys = (4 / 15) * (Current number of boys + Current number of girls)

  7. Subtract the current number of boys from the target number of boys to find out how many boys need to leave the room: Number of boys need to leave = Target number of boys - Current number of boys.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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