Question 983474
let g = original no. of girls
let b = original no. of boys
:
there were 1518 boys and girls in a hall.
g + b = 1518
when 2/3 of the boys and 1/5 of the girls left there were twice as many girls as boys remaining.
That means that 4/5 of the girls and 1/3 of the boys remained, so we can say
{{{4/5}}}g = 2({{{1/3}}}b)
{{{4/5}}}g = {{{2/3}}}b
multiply by 15 to get rid of the denominators
3(4g) = 5(2b)
12g = 10b
Simplify divide by 2
6g = 5b
b = {{{6/5}}}g
b = 1.2 g
in the 1st equation replace b with 1.2g
g + 1.2g = 1518
2.2g = 1518
g = 1518/2.2
g = 690 girls originally
then
1518 - 690 = 828 boys originally
:
:
Check this, by finding the remaining girls and boys
1/3 * 828 = 276 boys remain
4/5 * 690 = 552 girls
2 * 276 = 552 twice as many girls as boys