Question

The number of boys is `2/3` of the number of girls in a concert. There are `30` more girls than boys. How many children are there at the concert?

Answer 1

Number of boys `=60`

Number of girls `=90`

Explanation:

Let `B` & `G` be number of boys & girls respectively then we have

Condition 1:

`B=2/3G\ ........(1)`

Condition 2:

`G=B+30\ ........(2)`

Substituting value of `B` from (1) in (2) as follows

`G=2/3G+30`

`G/3=30`

`G=3\cdot 30`

`G=90`

setting `G=90` in (1), we get number of boys

`B=2/3(90)`

`=60`

Answer 2

There are `90` girls and `60` boys, giving a total of `150` children.

Explanation:

The number of boys is two-thirds of the number of girls.

The number of girls is therefore three-thirds.

`3/3 -2/3 =1/3`

The `30` girls more than the boys represents `1/3`

If `1/3` of the total is `30`, then `3/3` will be:

`3xx 30 =90`

Girls: `3xx30 = 90`

Boys: `2/3 xx90 = 60`

`90+60=150` children in total.