Question

The ratio of X to Y in a room is 6:5. If three boys leave the room, the ratio is 1:1. How many Y are in the room?

Answer 1

15 Y (girls) in the room

Explanation:

Given an initial ratio of boys : girls = 6 : 5 that becomes 1 : 1 when 3 boys leave the room, you want to know the number of girls in the room.

Ratio units

The initial difference in the number of ratio units is 6 -5 = 1. Removing 1 ratio unit from the "boys" side makes the ratio 5 : 5 = 1 : 1.

So, that 1 ratio unit corresponds to 3 boys. There are 5 ratio units of girls, so 3·5 = 15 girls.

There are 15 girls (Y) in the room.

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Alternative solution

You could write an equation or two:

b/g = 6/5 . . . . . . initial ratio of boys/girls

(b-3)/g = 1/1 . . . . final ratio of boys/girls

Solving the first for b gives

b = 6/5g

Using that in the second gives ...

(6/5g -3) = g . . . . . . substitute for b, multiply by g

1/5g = 3 . . . . . . . . add 3-g

g = 15 . . . . . . . multiply by 5