# 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?

Jun 28, 2018

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:

$0.4 b + 0.7 g = 27$

Moreover, we know that the ratio between boys and girls is $\frac{3}{2}$. This can be written as

$\frac{b}{g} = \frac{3}{2}$

$b = \frac{3}{2} g$

substitute this expression in the one we wrote before to get

$0.4 b + 0.7 g = 27 \setminus \iff 0.4 \left(\frac{3}{2} g\right) + 0.7 g = 27$

you can reduce the equation to get

$1.3 g = 27$

and thus

$g = \frac{27}{1.3} \setminus \approx 20.8$

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

$b = \frac{3}{2} g \approx \frac{3}{2} \cdot 20.8 = 31.2$

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