# A car used 14.7 gallons of gas while travellng 282.8 miles. About how many miles per gallon did the car average?

Nov 22, 2015

Number of miles traveled on one gallon is $18.5578$ to 4 decimal places$\to 18.6$ to 1 decimal place

#### Explanation:

The method clue is in the format of the units used in the answer.

You require 'miles' $\textcolor{b l u e}{\text{per}}$ 'gallon'.

That is: the number of miles for 'one' gallon. The use of 'per' means 'for each'

Ok! We will solve this by using ratio.

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Let the number of miles traveled on 1 gallon be $x$

$\left(\text{total miles")/("total gallons") = ("number of miles for one gallon")/("1 gallon}\right)$

$\frac{272.8}{14.7} = \frac{x}{1}$

So as we are using ratio we need to change 14.7 in $\frac{272.8}{14.7}$ to 1

We do this by dividing by its own value. But what we do to 'the bottom' we need to do the same to 'the top'.

$\frac{272.8 \div i \mathrm{de} 14.7}{14.7 \div i \mathrm{de} 14.7} \approx \frac{18.5578 \ldots}{1}$

So $x = 272.8 \div i \mathrm{de} 14.7 = 18.5578$ to 4 decimal places

color(blue)(~~~~~~~~~ " Useful mathematical method " ~~~~~)
This method can be used to change ratios into any values you wish. This will work as long as the denominator has the same relative proportion to the numerator!!!

So how far would you travel on 2 gallons $\to \frac{18.5578 \times 2}{1 \times 2}$

Or for greater precision $\frac{\textcolor{b r o w n}{\left(272.8 \div i \mathrm{de} 14.7\right)} \times 2}{\textcolor{b r o w n}{\left(14.7 \div i \mathrm{de} 14.7\right)} \times 2}$