Question

The amount of money it takes to fill up your gas tank varies directly with the number of gallons you buy. You spent $16.56 to fill up your car with gasoline. If you bought 6 gallons of gasoline, what is the constant of variation

Answer 1

Let "m" represent the money required.

Let "n" represent the number of gallons filled.

Since it is given to us that the amount of money it takes to fill up your gas tank varies directly with the number of gallons you buy, therefore, this can be written mathematically as:

$m\propto n$

We know that when we remove the "varies to" sign we have to replace it with the equal to sign and the constant of variation, which we will represent by the letter "k".

Therefore the above expression will become:

$m=k\times n$

Now, it is given that m=$16.56 and n=6 gallons

Therefore, $16.56=k\times 6$

Dividing both sides by 16.56 we get:

$\therefore k=\frac{16.56}{6}=2.76$

Thus, k=2.76 $/gallon is the value of the constant of variation.

Answer 2

The constant of variation is 2.76 dollars per gallon