Problema Solution
A gas station charges $2.30 per gallon, and $8 for a car wash. If drivers fill-up their cars and get a car wash, the gas station reduces the charge per gallon of gas to $2.20. The gas station manager has noticed that this incentive motivates more drivers to get a car wash. Assume that the average motorist buys 12 gallons of gas per visit to the gas station, and that five out of a hundred motorists would also get a car wash without the advertised incentive. (A) Under those normal conditions, how much money does the gas station take in for every hundred motorists? (B) How many additional car washes would be necessary to at least break even, if gas is lowered by 10 cents a gallon (assuming that the profit on a car wash is negligible)?
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(A)
Under normal conditions, the money the gas station takes per 100 motorists is:
2.30*12*100 + 8*5 = $2,800
(B)
Let 'x' represent the number of additional car washes:
(2.30 - 0.10)*12*100 + 8*(5 + x)=2,800
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click here to see the equation solved for x
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x = 15 cars
In other words, the number of car washes would have to increase from 5 to 15+5=20 out of every 100 motorists who utilized the gas station in order for this incentive to break even.
More than 20 motorists would have to purchase car washes in order for this gas station to justify reducing the price of gasoline (at least break even).