Question

The gas mileage of a car is 28.16 miles per gallon. how many gallons per mile is this?

Answer 1

`1` gallon per `25/704` miles, or `1` gallon per about `0.0355` miles

Explanation:

We can set up a proportion :

`28.16/1 = 1/x`

We don't want decimals in a fraction, so multiply `1/28.16` by `100/100 (=1`).

`28.16/1*100/100`

`2816/100`

Now simplify:

`(2816-:4)/(100-:4)`

`704/25`

Back to the equation:

`704/25 = 1/x`

Cross-multiply:

`704x=25*1`

Divide both sides by `704`:

`x=25/704` or about `0.0355`

So, the answer is `25/704` or `0.0355` about gallons per mile.

Answer 2

An alternate approach...

Explanation:

We're told that we have a car that uses 1 gallon of gas to go 28.16 miles:

`"miles"/"gallon"=28.16/1`

What we want to know is how many gallons per mile:

`"gallon"/"miles"`

We already know the ratio, `28.16/1`, so we need to invert the fraction:

`1/28.16~~0.0355` gallons per mile

Answer 3

28.16 miles per gallon

Written mathematically we have:

28.16 miles = 1 gallon

Dividing by 28.16 on both sides we get:

1 mile = `(1-:28.16)` gallons

or, 1 mile = 0.0355114 gallons

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Answer 4

Approximately `0.0356" mpg"` to 4 decimal places
Exactly `27/704" mpg"`

Explanation:

The lovely thing about ratios when in the format of a fraction is that you can manipulate them into any form you wish. That is, as long as you follow the 'rules' of mathematics.

Consider the wording: mile per gallon. This is a unit of measurement and is actually in the fraction format
`("miles")/("gallons") -> m/g`

The word per means 'for each' so 'miles per gallon' means; how many miles can you travel for 1 gallon.

So we have as given: `("miles")/("gallons")->28.16/1`

However, we need 'gallons per mile' so we can 'flip' the units of measurement upside down (invert it). Giving:

`("gallons")/("miles")->1/28.16`

The target for this is gallons per mile. So we naeed to change the 28.16 miles into the value of 1.

For multiply or divide in fractions or fraction format, what we do to the bottom we also do to the top.

We need to change the 28.16 into 1 so we divide it by itself.

`("gallons")/("miles")->1/28.16 -=(1-:28.16)/(28.16-:28.16) = (0.0355113...)/1`

Rounding this to 4 decimal places we have

`("gallons")/("miles")=0.0356/1`

We don't bother with the one as it is understood to be there. So we end up with:

`("gallons")/("miles")=0.0356` to 4 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that the decimal is not precise. As a fraction we have

`("gallons")/("miles")->1/28.16 ->(1xx100)/(28.16xx100) = 100/2816 = 25/704`

So we have `27/704" miles per gallon"`

As a check: `27-:704 ~~0.0355113...`