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

An illustration of the letter 'A' in a speech bubbles

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
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial