# My fuel is at 80% full. After traveling some distance, only 30% of that fuel is left. I fill the tank to full capacity by putting in 19 gallons. What is the full capacity of my tank?

Aug 28, 2016

25 gallons

#### Explanation:

First you have to find what percent of the tank is left after 30% of 80% of the fuel has been spent

multiply 80% xx 30% = 24% of the tank is left.

now subtract 100% - 24% = 76% of the tank has been used.

$$ 76% of the tank equals  19 gallons

set up a ratio


$\frac{76}{100} = \frac{19}{x} \text{ multiply both sides by } 100 x$

$\left(100 x\right) \times \frac{76}{100} = \left(100 x\right) \times \frac{19}{x}$ this gives

$76 \times x = 100 \times 19$

Now divide both sides by 76

$\frac{76 x}{76} = \frac{1900}{76}$ this gives

$x = 25$

Aug 29, 2016

Full tank capacity is 25 gallons

#### Explanation:

The only thing we are interested is the tank. Not the distance travelled.

The tank has 30% of its original content left.

Thus the amount of fuel left is 30% of 80%

Amount of the whole tank taken up by fuel is:

30/100xx80/100 = 24/100 -=24%

So the free space left in the tank by volume is
100%-24% = 76% ->76/100

We know that it takes 19 gallons to fill up the 76% volume left.

So by ratio we have:

$\left(\text{19 gallons")/("76% volume")-=("Full volume in gallons")/("100% volume}\right)$

To change 76 into 100 we multiply it by $\frac{100}{76}$ but as this is a ratio we must also multiply the top value the same way.

$= \frac{19 \times \frac{100}{76}}{74 \times \frac{100}{76}} = \frac{25}{100} \to \left(\text{25 gallons")/("full tanks}\right)$