Question

A new day care center has a maximumcapacity of 320 people. The staff-to-childratio is 3:5. The number of children willgrow by 20 each year. In how many yearswill the center reach full capacity?

Answer 1

if the day care center started with 0 children ,we have that

$\begin{gathered} \frac{3}{5}x+x=320\rightarrow \\ \frac{8}{5}x=320 \\ x=320\cdot\frac{5}{8} \\ x=200 \end{gathered}$

It will reach it's limit when they get 200 children, so

$t=\frac{200}{20}=10$

so after 10 years it will reach full capacity