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?

Expert Answers

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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;


`= 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
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