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} (3)/(5)x+x=320\rightarrow \\ (8)/(5)x=320 \\ x=320\cdot(5)/(8) \\ x=200 \end{gathered}`

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

`t=(200)/(20)=10`

so after 10 years it will reach full capacity