Question

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?

Answer 1

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

`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`

Answer 2

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:

`("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")`