Question

1) Decide whether the table could represent a proportional relationship. Show your work. The cost of fountain drinks at Hot Dog Hut. volume (fluid ounces) cost ($) 16 $1.49 20 $1.59 30 $1.89

Answer 1

If the table represents a proportional relationship between the cost of the drinks and the size of drinks, then each ordered pair shown in the table should be at the same ratio.

Let "y" represent the cost of the drink and "x" represent the size of the drink, a proportional relationship between both of them can be expressed as:

`y=kx`

The constant of proportionality, k, can be calculated as

`k=(y)/(x)`

- First ordered pair (16,1.49):

`\begin{gathered} k=(1.49)/(16) \\ k=0.093125 \end{gathered}`

- Second ordered pair (20,1.59):

`\begin{gathered} k=(1.59)/(20) \\ k=0.0795 \end{gathered}`

- Third ordered pair (1.89,30):

`\begin{gathered} k=(1.89)/(30) \\ k=0.063 \end{gathered}`

The cost and sizes of the drinks are not in a proportional relationship.