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

100

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 (x)/(y -25)= (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 (x - 15)/(y -25) = (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