Justin drove miles using gallons of gas. At this rate, how many miles would he drive using gallons of gas?

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dpaden | Elementary School Teacher | (Level 1) Adjunct Educator

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This is a rate problem so it can be solved by setting the known rate equal to the unknown rate and solving for the variable.  The know rate is the miles per gallon that Justin drove or miles (m) divided by gallons (g).

`m/g`

The unknown is the miles he could drive given a second quantity of gas or the unknown miles (x)  divided by the new gallons (ng).

`x/(ng)`

Setting these equal,

`(m/g) = (x/(ng))`

You can solve by cross multiplying.  This is the simplified method of multiplying both sides by the product of the denominators, in this case.  The denominators then cancel out.

`g*ng`

This gives you

m*ng = x*g

Solving for x  by dividing both sides by g, you are left with

` ((m*ng)/g) = x `

In short, you multiply the known miles by the new quanity of gas and divide the result by the first or known gas, that gives you the miles that can by driven.

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