Question

Some boys and girls are waiting for school buses. 25 girls get on the first bus. The ratio of boys to girls at the stop is now 3:2. 15 boys get on the second bus. There are now the same number of boys and girls at the bus stop. How many students were originally at the bus stop?​

Answer 1

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:

        $\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------$(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,

     $\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25$

             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

                 $\sf \boxed{\bf y = 55}$

Plugin y = 55 in equation (I)

       x = 55 -10

        $\sf \boxed{\bf x = 45}$

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100