Question

A map has the scale 0.75 of an inch equals 150 miles. The distance from Springfield to Glenview is 3.75 inches. How many actual miles separate Springfield from Glenview?

Answer 1

`750` miles

Explanation:

Measurements with a scale are always in direct proportion, regardless what units are used, as long as you compare the correct parts.

`"inches"/"miles" : 0.75/150 = 3.75/x" "larr` cross multiply

`0.75x = 150xx3.75`

`x = (150xx3.75)/0.75`

`x = 750` miles

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You can also find how many miles are represented by 1 inch:

`150` miles are represented by `0.75` inches

`150/0.75` miles are represented by `1` inch

`200` miles are represented by `1` inch

So, a length of `3.75` inches represents:

`3.75 xx 200 = 750` miles

Answer 2

Slight alternative method.

750 miles

Explanation:

Using ratio in fraction form

`"inches"/"miles" -> 0.75/150 = 3.75/x larr" Same starting point as Ez as pi"`

Consider the top numbers (numerators)

We have `0.75 ->3.75`

To change 0.75 into 3.75 we do `0.75xx5`

Multiply by 1 and you do not change the value. However 1 comes in many forms so you can change the way something looks but not change its inherent value.

`"inches"/"miles" ->color(green)(0.75/150color(red)(xx1)" " =" " 0.75/150color(red)(xx5/5)`

`color(green)(" "=" "3.75/750)`

`color(purple)("So 3.75 inches is the equivalent of 750 miles.")`
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Note that `0.75-:150" "=" "3.75-:750`

So I should get 1 if I do the following:

`0.75/150 -:3.75/750`

`0.75/150xx750/3.75`

`0.75/3.75xx750/150`

`1/5xx5/1 = 1`

Answer 3

750 miles

Explanation:

`0.75`inches = `150`miles
`3.75`inches =`3.75/0.75 xx 150 = 750`miles