Question

At a movie night,1/4 of the persons were boys,5/8 were girls and the rest were adults.If there were 56 more girls than adults how many persons were in total?

Answer 1

Given:

Number of boys =
`(1)/(4)` of the total persons.

Number of girls =
`(5)/(8)` of the total persons.

Remaining persons are adults.

There were 56 more girls than adults.

To find:

The number of total persons.

Solution:

Let x be the number of total persons. Then,

Number of boys =
`(1)/(4)x`

Number of girls =
`(5)/(8)x`

Number of adults = Total persons - Boys - Girls

=
`x-(1)/(4)x-(5)/(8)x`

=
`(8x-2x-5x)/(8)`

=
`(x)/(8)`

There were 56 more girls than adults.

Girls = Adults + 56

`(5)/(8)x=(x)/(8)+56`

`(5)/(8)x-(x)/(8)=56`

`(4)/(8)x=56`

`(1)/(2)x=56`

Multiply both sides by 2.

`x=112`

Therefore, the total number of persons is 112.