Find the number of boys and girls involved the project of increased to 75%?

Question

"A professor started a project with a group of student 60% of work were boys due to some unavoidable read six girls could not turn up so the professor had to meet some changes in the group.he admitted six boys. I doing so the percentage of boys in the project. Find the number of boys and girls involved the project of increased to 75%

Answer 1

B = number of boys
G = number of girls in initial group

If 60% of the group are boys, then

B = .60 ( B + G )

But then we lose six girls and now 75% of the group are boys:

B = .75 ( B + G - 6 )

Now we have two equations and two unknowns.

Use the first and isolate B:

B = .60 ( B + G )
B = .60 B + .60 G
.40 B = .60 G
B = ( .60 / .40 ) G

Then substitute into the second:

B = .75 ( B + G - 6 )
B = .75 B + .75 G - ( .75 ) ( 6 )
.25 B = .75 G - ( .75 ) ( 6 )
B = ( .75 / .25 ) G - ( .75 ) ( 6 ) / ( .25 )

( .60 / .40 ) G = ( .75 / .25 ) G - ( .75 ) ( 6 ) / ( .25 )
( .60 ) ( .25 ) G = ( .75 ) ( .40 ) G - ( .75 ) ( 6 ) ( .40 )
( .15 ) G = ( .30 ) G - ( .75 ) ( 6 ) ( .40 )
( .75 ) ( 6 ) ( .40 ) = ( .15 ) G
( .75 ) ( 6 ) ( .40 ) / ( .15 ) = G

So after all that, G = 12 so B = 18

The original group of 30 had 18 boys.
The final group still has 18 boys but only 24 girls.