# There 96 girls at a party. The ratio of girls to boys is 4:5. More boys arrived and the ratio became 2:3. How many boys arrived?

There are 96 girls.

The ratio of girl to boy is 4:5

If there is 9 in total at a ratio of 4:5 then there will be 4 girls and 5 boys.

So if there is 96 girls;

G:B

`= 4:5`

`= 4xx24:5xx24`

`= 96:120`

So initially there...

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There are 96 girls.

The ratio of girl to boy is 4:5

If there is 9 in total at a ratio of 4:5 then there will be 4 girls and 5 boys.

So if there is 96 girls;

G:B

`= 4:5`

`= 4xx24:5xx24`

`= 96:120`

So initially there were 120 boys.

Now let us say x number of boys arrived.

Total boys = 120+x

Total girls = 96

`G:B = 96:(120+x)`

But it is given that the G:B ratio is 2:3 at the end.

`96:(120+x) = 2:3`

Usually a ratio means the division or fraction of numbers.

`96/(120+x) = 2/3`

`96xx3 = 2(120+x)`

`x = 24`

So 24 boys has arrived.

Approved by eNotes Editorial Team