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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?

Respuesta :

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

[tex]\begin{gathered} \frac{3}{5}x+x=320\rightarrow \\ \frac{8}{5}x=320 \\ x=320\cdot\frac{5}{8} \\ x=200 \end{gathered}[/tex]

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

[tex]t=\frac{200}{20}=10[/tex]

so after 10 years it will reach full capacity

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