Question

1. Jessica spent many days at the city park last summer. She noticed that 4 out of every 15 flying insects she saw at the park were butterflies. Number of Insects insects Number of Butterflies butterflies

Answer 1

Let:

x = Number of insects

y(x) = Number of butterflies

k = constant of proportionality

She noticed that 4 out of every 15 flying insects she saw at the park were butterflies, therefore:

`\begin{gathered} y(x)=k\cdot x \\ x=15 \\ y(x)=4 \\ 4=k\cdot15 \\ \text{Solving for k:} \\ k=(4)/(15) \end{gathered}`

Therefore, the function which represents this situation is:

`y(x)=(4)/(15)x`