Question 279669
Let {{{b}}} = number of boys in the beginning
Let {{{g}}} = number of girls in the beginning
15 girls leave, so
{{{b + (g - 15)}}} in the group
There are 2 boys for each girl, so
{{{b = 2*(g - 15)}}}
45 boys leave, so
{{{(b - 45) + (g - 15)}}} in the group
Now there are 5 girls for each boy, so
{{{g - 15 = 5*(b - 45)}}}
{{{g - 15 = 5b - 225}}}
{{{5b = g + 210}}}
{{{b = (g + 210)/5}}}
I'll substitute this into {{{b = 2*(g - 15)}}}
{{{(g + 210)/5 = 2g - 30}}}
{{{g + 210 = 10g - 150}}}
{{{9g = 360}}}
{{{g = 40}}}
There were 40 girls in the beginning- (A)
check:
{{{b = 2*(g - 15)}}}
{{{b = 2*(40 - 15)}}}
{{{b = 2*25}}}
{{{b = 50}}} and {{{g = 40}}} in the original group
15 girls leave, so
{{{b = 50}}}, {{{g = 25}}}
There are 2 boys for each girl- that checks
45 boys leave, so
{{{b = 5}}}, {{{g = 25}}}
There are 5 girls for each boy- OK