Question

Every package of a certain toy also includes 2 batteries. Are the number of toys and number of batteries in a proportional relationship?If so, what are the two constants of proportionality? If not, explain your reasoning.

Answer 1

We have the statement "Every package of a certain toy also includes 2 batteries" and we need to answer if the relationship between batteries and toys is proportional.

The answer is YES, because from the statement we know that there is one toy for package and two batteries for package, so the relationship between toys and batteries is:

`\begin{gathered} k_1=1\frac{toy}{\text{package}} \\ k_2=2\text{ }\frac{\text{batteries}}{\text{package}} \\ k_3=\text{ }\frac{\text{number of toys}}{\text{number of batteries}}=(k_1)/(k_2) \\ k_3=\frac{1\frac{toy}{\text{package}}}{2\text{ }\frac{\text{batteries}}{\text{package}}}=0.5(toy)/(batteries) \end{gathered}`

The two constants of proportionality are k1 and k2.