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A power company is going to locate it's new power plant along a road connecting the towns of Exton and Whyton which are 10 miles apart. For political reasons, the power company will buy coal from both towns. The price of coal per ton from Exton is $26.65 plus $.45 per mile for delivery. The price per ton from Whyton is $26.25 plus $.25 per mile for delivery. How far from Exton should the plant be located if the price of coal per ton delivered from Exton is to be equal to that from Whyton?
We want to write an equation that shows the price per ton from each town is equal
Let x = location distance from Exton
(10-x) = location distance from Whyton
Cost/ton Exton = Cost/ton Wyton
.45x + 26.65 = .25(10-x) + 26.25
.45x + 26.65 = 2.5 - .25x + 26.25
.45x + .25x = 2.5 + 26.25 - 26.65
.7x = 2.10
x = 3 miles from Exton
We can prove this, (location is 7 mi from Whyton)
7(.25) + 26.25 = $28
3(.45) + 26.45 = $28 also