Question

any letters or words in your answer! Ciera works at a day care center. Her job is to make sure there are always enough adult workers. Last month, there were 7 adults for 56 children, which is the minimum ratio allowed under state law. This month, 74 children are expected to enroll. How many adults will there need to be at the center? Your answer

Answer 1

10 adults

Explanation

Step 1

find the unit rate

$\text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}$

Let

number of children=56

number of adults=7

replace,

$\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}= \\ \text{unit rate=}\frac{56\text{ Children}}{7\text{ adults}} \\ \text{unit rate= 8 Children per adult} \end{gathered}$

Step 2

Let x represents the adults needed for 74 children

find the unit rate:

$\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}} \\ \text{unit rate=}\frac{74}{x} \end{gathered}$

as the unit rate must be the same

$\begin{gathered} 8\frac{Children}{\text{adult}}=\frac{74}{x} \\ 8=\frac{74}{x} \\ cross\text{ multiply} \\ 8x=74\cdot1 \\ 8x=74 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{74}{8} \\ x=9.25 \\ \text{hence, we n}eed\text{ 10 adults at the center} \end{gathered}$