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

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

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Answer 1 · 2017-07-03T10:10:53

$Full tank = 35 gallons$ $"Full tank"=35" gallons"$

Explanation:

$Total rewrite$ $color(brown)("Total rewrite")$

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

So we have:

$Full tank \times \frac{2}{5} = 14 gallons$ $"Full tank"xx2/5=14" gallons"$

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

$Full tank \times \frac{2}{5} \times \frac{5}{2} = 14 \times \frac{5}{2} gallons$ $color(green)("Full tank"xx2/5color(red)(xx5/2)=14color(red)(xx5/2)" gallons")$

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

$Full tank \times \frac{2}{2} \times \frac{5}{5} = 14 \times \frac{5}{2} gallons$ $color(green)("Full tank"xx2/(color(red)(2))color(red)(xx5/(color(green)(5))=14color(red)(xx5/2)" gallons")$

$Full tank \times 1 \times 1 = 7 \times 5$ $"Full tank"xx1xx1=7xx5$

$Full tank = 35 gallons$ $"Full tank"=35" gallons"$

Answer 2 · 2017-07-03T10:13:22

$(\frac{2}{5}) X = 14$ $(2/5)X = 14$ 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:

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

$X = \frac{14 \times 5}{2}$ $X = (14times5)/2$

$X = 35$ $X= 35$ gallons.

The full capacity of the tank is 35 gallons.

Answer 3 · 2017-07-04T18:49:04

$35$ $35$ gallons = full tank.

Explanation:

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

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

$\frac{\frac{5}{5}}{\frac{2}{5}} \times \frac{14}{1}$ $(5/5)/(2/5) xx 14/1$

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

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

Answer 4 · 2017-07-06T20:55:32

$35$ 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

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

4 Answers

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Sara puts 141414 gallons of fuel into the tank of her car and finds that it is then 2/5252/5 full. How much fuel does the tank hold when full?

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Explanation:

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