Ratio Problem (Help needed)

Hi there, I'll give it a try.

Lets assume that the initial number of boys and girls be x & y respectively. Now, as per the question, the ratio of boys to girls is 2 to 5, ie; ratio of x to y is 2 to 5 which can be written mathematically as x/y=2/5 ==> 5x=2y ==> 5x-2y=0 ----Let this be our equation 1

Now, when we add 12 more boys, the number of boys becomes x+12. the number of girls remains unchanged at y itself. Now, as the new ratio is 4 to 9, it can be written as (x+12)/y=4/9 ==> 9(x+12)=4y
==> 9x-4y=-108 ---equation 2.

Once we solve for x using equation 1 and 2, we will get the value of x=108.

Hope this helps!!

I understand it! thank you so much! I hope you reach your desired score and beat the gmat!

Christine4lakers wrote:Hi, I am new to the forum. I am sorry if this is the wrong place to post my question, but i am having a hard time with ratio problems. Can i get an explanation on how to figure out this problem. Please explain step by step. I am a visual learner and skipped steps really mess me up. I would really appreciate the help

The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were
added to the school, the new ratio of boys to girls would be 4 to 9. How many boys
currently attend the school?

The answer key says 108 is the answer, but i don't know how to arrive at that solution

b/g = 2/5

5b = 2g

b+12/g = 4/9

9b+ 108 = 4g

since 2g =5b, then 4g = 10b

9b + 108 = 10b

b = 108