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?

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

`76/100 = 19/x " multiply both sides by " 100x`

`(100x ) xx76/100 = (100x ) xx 19/x` this gives

`76 xx x = 100 xx 19`

Now divide both sides by 76

`(76 x) / 76 = 1900/76` this gives

`x = 25`

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:

`("19 gallons")/("76% volume")-=("Full volume in gallons")/("100% volume")`

To change 76 into 100 we multiply it by `100/76` but as this is a ratio we must also multiply the top value the same way.

`=(19xx100/76)/(74xx100/76) = 25/100 -> ("25 gallons")/("full tanks")`