Answer:
100
Step-by-step explanation:
Forming algebraic equations and solving:
Let the number of boys originally at the stop = 'x'
Let the number of girls originally at the stop = 'y'
25 girls get on the first bus.
⇒ The number of girls now at the stop = y -25
Ratio of boys to girls:
[tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)
15 boys get on the second bus.
Now, the number of boys at the stop = x - 15
Number of girls at the stop = y - 25
Ratio of boys to girls,
[tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]
x = y -25 + 15
x = y - 10
Plugin x = y - 10 in equation (I)
2*(y-10) = 3y -75
2y - 20 = 3y -75
-20 = 3y - 75 - 2y
-20 = y -75
-20 +75 = y
[tex]\sf \boxed{\bf y = 55}[/tex]
Plugin y = 55 in equation (I)
x = 55 -10
[tex]\sf \boxed{\bf x = 45}[/tex]
Number of students originally at the stop = x + y
= 55 + 45
= 100
