A car can travel 476 miles on 14 gallons of gas. How do you write equation relating the distance d to the number of gallons g. How many gallons of gas does this car need to travel 578 miles?

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Answer 1 · 2017-05-24T01:21:34

#17" gallons"#

You are given that traveling #476# miles consumes #14# gallons of gas. You can rewrite this as a formula:

#476xxd=14xxg#

You can divide both sides by #14# to get

#476/14 d=1xxg#

#34xxd= 1xxg#

That is, #1# gallon will take you #34# miles (or #34# mpg)

This gives us a conversion factor which can be expressed in one of two ways:

Either #(34" miles")/(1" gallon")# or #(1" gallon")/(34" miles")#

If you are given gallons, use the first one. If you are given miles, use the second one. You are given miles, so

#578cancel(" miles")xx(1" gallon")/(34cancel(" miles"))=17" gallons"#