<PRE><B>Question 247114</B>
There is a group of boys and girls standing in line at the bus stop.
Let g = no. of girls
Let b = no. of boys
:
 15 girls get on the first bus to arrive; now there are 2 boys for each girl still at the bus stop.
{{{b/(g-15)}}} = 2
b = 2(g-15)
b = 2g - 30
:
On the second bus, 45 boys get on; now, at the bus stop, there are 5 girls for each boy.
{{{(b-45)/(g-15)}}} = {{{1/5}}}
cross multiply
5(b-45) = g - 15
5b - 225 = g - 15
5b = g - 15 + 225
5b = g + 210
:
Replace b with (2g-30) from the 1st equation
5(2g - 30) = g + 210
10g - 150 = g + 210
10g - g = 210 + 150
9g = 360
g = {{{360/9}}}
g = 40 girls originally at the bus stop
:
:
To check solution find the no. of boys
b = 2(40) - 30
b = 50 boys
:
{{{(50 - 45)/(40-15)}}} = {{{5/25}}} = {{{1/5}}}



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