Question

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?

Answer 1

`"Full tank"=35" gallons"`

Explanation:

`color(brown)("Total rewrite")`

`color(blue)("The only way this can work is if we assume that the tank was empty before the 14")` `color(blue)("gallons were poured in the tank. Not stated in the question.")`

So we have:

`"Full tank"xx2/5=14" gallons"`

Multiply both sides by `5/2`. This gets the 'Full tank' part on its own.

`color(green)("Full tank"xx2/5color(red)(xx5/2)=14color(red)(xx5/2)" gallons")`

Consider the example of `2xx3=3xx2=6`. We can 'swap' things round when multiplying. So using this we write:

`color(green)("Full tank"xx2/(color(red)(2))color(red)(xx5/(color(green)(5))=14color(red)(xx5/2)" gallons")`

`"Full tank"xx1xx1=7xx5`

`"Full tank"=35" gallons"`

Answer 2

`(2/5)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:

`(2/5)X = 14`

`X = (14times5)/2`

`X= 35` gallons.

The full capacity of the tank is 35 gallons.

Answer 3

`35` gallons = full tank.

Explanation:

`2/5` of full tank `= 14` gallons

`5/5` of tank =?

`(5/5)/(2/5) xx 14/1`

`5/cancel5^1 xx cancel5^1/cancel2^1 xx cancel14^7/1`

`7 xx 5=35=5/5=35` gallons= full tank

Answer 4

`35` gallons

Explanation:

Let's look at the fraction `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,

`:. 5 xx7 =35` gallons