Question

At a corner gas station, the revenue R varies directly with the number of gallons g gas sold. If the revenue is $36 when the number of gallons sold is 10, find the linear equation that relates revenue R to the number gallons of gas sold is 15.5?

Answer 1

Hello there. To solve this question, we have to remember some properties about proportionality,

Given that the revenue R varies directly with the number g of gallons of gas sold, we know that they follow the equation

`R=k\cdot g`

where k is the proportionality constant.

We know that when the number of gallons sold is 10, then the revenue is $36.

With this, we can determine the constant k:

Plugging the values, we get

`36=k\cdot10`

Divide both sides of the equation by a factor of 10

`k=(36)/(10)=3.6`

Hence the equation turns into

`R=3.6\cdot g`

To determine what will be the revenue R when the number of gallons sold is 15.5, the linear equation is simply:

`R=3.6\cdot15.5=\$55.8`