Question

40% of the boys, 70% of the girls in a class attend a picnic and ratio of boys to girls in the class is 3:2 if the number on the picnic was 27. How many are there in the whole class?

Answer 1

The total is approx. `52` students. It seems a little bit odd that the result is not an integer, given the nature of the problem, but I don't think I did anything wrong.

Explanation:

Let `b` be the number of boys and `g` be the number of girls. We know that `40%` of the boys and `70%` of the girls attended the picnic, and there were `27` students overall. This leads to the following equation:

`0.4b+0.7g = 27`

Moreover, we know that the ratio between boys and girls is `3/2`. This can be written as

`b/g=3/2`

which leads to

`b=3/2g`

substitute this expression in the one we wrote before to get

`0.4b+0.7g = 27 \iff 0.4(3/2g)+0.7g = 27`

you can reduce the equation to get

`1.3g=27`

and thus

`g = 27/1.3 \approx 20.8`

Plug this result in the boys-to-girl ratio to get

`b = 3/2g approx 3/2 * 20.8 = 31.2`

So, the total is `b+g approx 20.8 + 31.2 = 52`