Question

lily is starting a summer camp for children who are deaf or hard of hearing. she needs to hire enough counselors to chaperone the children. there is a proportional relationship between the number of counselors lily hires, x, and the maximum number of children who can attend the camp, y.

x (counselors)	y (maximum number of children)
3	12
4	16
5	20

what is the constant of proportionality? write your answer as a whole number or decimal. children per counselor

Explanation:

Step1: Recall proportion formula

For a proportional relationship $y = kx$, where $k$ is the constant of proportionality. We can find $k$ by $\frac{y}{x}$.

Step2: Select a data - pair

Let's take the first pair $x = 2$ and $y = 8$.

Step3: Calculate the constant

$k=\frac{y}{x}=\frac{8}{2}=4$. We can check with other pairs. For $x = 3,y = 12$, $\frac{y}{x}=\frac{12}{3}=4$; for $x = 4,y = 16$, $\frac{y}{x}=\frac{16}{4}=4$; for $x = 5,y = 20$, $\frac{y}{x}=\frac{20}{5}=4$.

Answer:

4