When 5 new girls joined the class the percent of girls increased from 40 percent to 50 percent what is the number of boys in the class?

Answer 1

Let us use the letter G for the number of girl in the class and B for the number of boy.

The total number of students is B+G. We are told the original percent of girls went from 40 to 50 %.

So when there was 40% girls, we had G/(B+G) =.4 Now we add 5 new girls and the percent of girls is .5

So

(G+5)/(B+G+5)=.5

Let's cross multiply the first equation and we have

.4G+.4B= G or

.4B=.6G

B=(3/2)G

The second equation becomes (G+5)=(1/2)G+(1/2)B+(5/2)

This is the same as

2G+10=G+B+5

Or

G=B-5

Now plug in B=(3/2)G

G=(3/2)G-5 or

-1/2 G=-5

or

G=10 This means B was (3/2)x10=15.

So at first we had

10/25 girls or 40% then when we added 5 girls we have

15/30 girls or 50%

So in the original class we had 10 girls and 15 boys and then we had 15 girls and 15 boys.

This could be done without the equations, since the numbers are pretty easy in this case. But this method works for any numbers.