# Sara puts 14 gallons of fuel into the tank of her car and finds that it is then 2/5 full. How much fuel does the tank hold when full?

Jul 3, 2017

$\text{Full tank"=35" gallons}$

#### Explanation:

$\textcolor{b r o w n}{\text{Total rewrite}}$

$\textcolor{b l u e}{\text{The only way this can work is if we assume that the tank was empty before the 14}}$$\textcolor{b l u e}{\text{gallons were poured in the tank. Not stated in the question.}}$

So we have:

$\text{Full tank"xx2/5=14" gallons}$

Multiply both sides by $\frac{5}{2}$. This gets the 'Full tank' part on its own.

$\textcolor{g r e e n}{\text{Full tank"xx2/5color(red)(xx5/2)=14color(red)(xx5/2)" gallons}}$

Consider the example of $2 \times 3 = 3 \times 2 = 6$. We can 'swap' things round when multiplying. So using this we write:

$\textcolor{g r e e n}{\text{Full tank"xx2/(color(red)(2))color(red)(xx5/(color(green)(5))=14color(red)(xx5/2)" gallons}}$

$\text{Full tank} \times 1 \times 1 = 7 \times 5$

$\text{Full tank"=35" gallons}$

Jul 3, 2017

$\left(\frac{2}{5}\right) X = 14$ gallons. Full capacity of the tank is 35 gallons

#### Explanation:

At the beginning, the tank was empty, I assume.

Therefore, when Sara fills the tank with 14 gallons of water, the tank is 40 percent full.

Now you can get the full capacity of the tank:

$\left(\frac{2}{5}\right) X = 14$

$X = \frac{14 \times 5}{2}$

$X = 35$ gallons.

The full capacity of the tank is 35 gallons.

Jul 4, 2017

$35$ gallons = full tank.

#### Explanation:

$\frac{2}{5}$ of full tank $= 14$ gallons

$\frac{5}{5}$ of tank =?

$\frac{\frac{5}{5}}{\frac{2}{5}} \times \frac{14}{1}$

$\frac{5}{\cancel{5}} ^ 1 \times {\cancel{5}}^{1} / {\cancel{2}}^{1} \times {\cancel{14}}^{7} / 1$

$7 \times 5 = 35 = \frac{5}{5} = 35$ gallons= full tank

Jul 6, 2017

$35$ gallons

#### Explanation:

Let's look at the fraction $\frac{2}{5}$ first.

This means that the full amount has been divided into $5$ portions.
This is indicated as 'fifths'

TWO of these fifths is stated to be $14$ gallons. (assuming the tank was empty to start with.)

If $2$ parts represent $14$ gallons, then

$1$ part represents $14 \div 2 = 7$ gallons

The whole will be made of $5$ parts,

$\therefore 5 \times 7 = 35$ gallons