# In a fast-food restaurant, the ratio of people eating hamburgers to people eating chicken is 4 :3. There are 84 people in the reasturant. How many people are eating hamburgers and how many are eating chicken?

May 23, 2015

If we put $h$ as the number of people eating hamburger and $c$ the number of people eating chicken, then:

$4 : 3 = h : c$.

There is a property, called composition property, that says:

$a : b = c : \mathrm{dr} A r r \left(a + b\right) : a = \left(c + d\right) : c$

or:

$a : b = c : \mathrm{dr} A r r \left(a + b\right) : b = \left(c + d\right) : d$.

So:

$\left(4 + 3\right) : 4 = \left(h + c\right) : h \Rightarrow 7 : 4 = 84 : h \Rightarrow h = \frac{84 \cdot 4}{7} = 48$

$c = 84 - 48 = 36$.