Question 134490: angels car gets 32 miles per gallon and mos car gets 22 miles per gallon.when traveling from morgan run to clinton,they both used a whole number of gallons of gasoline.what is the closest that morgan run and clinton could be?how many gallons did angels car use?how many gallons did mos car use?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=number of gal used by angel
Then 32x=distance morgan run-clinton
And let y=number of gal used by mos
Then 22y also equals distance morgan run-clinton
So, our equation to deal with is:
32x=22y or
16x=11y divide each side by y(not equal to zero) and 16
x/y=11/16
What this tells us is that the ratio of the number of gal used by angel and the number of gal used by mos is 11/16 and this fraction cannot be reduced further which means that this represents the smallest amount of gas that each can use that satisfies the problem.
Closest distance between morgan run and clinton
32*11 or 22*16=352 mi
Amount of gas used by angel=11 gal
Amount of gas used by mos=16 gal
You can check this problem by verifying that there are not any pairs of numbers smaller than 11 and 16 that works: For example:
If x=1, then 16=11y--------------no
If x=2, then 32=11y-----------no
etc up to x=11
Hope this helps---ptaylor
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