Question 169602: The ratio of a fleet of small jeeps to laarge jeeps is 5 to 2. Fule consumption for the small jeeps is 800,000 gallons per trip. Fuel consumption for the large jeeps is 1100000 gallons per trip. If the fleet has a supply of 18,600,000 gallons How many small jeeps are assigned to the fleet.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i got an answer even though i'm not quite sure i understand the problem.
here's what i got.
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total number of gallons available is 18,600,000 (given)
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ratio of small jeeps to large jeeps is 5/2 (given)
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let S = number of small jeeps
let L = number of large jeeps
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S = 5/2 * L
this means that the number of small jeeps is 5/2 * the number of large jeeps.
if L = 100, then S = 5/2 * 100 = 500 / 2 = 250.
250/100 = 25/10 = 5/2 which is the given ratio of small jeeps to large.
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Fuel Consumption for the small jeeps is 800,000 gallons per trip.
Fuel Consumption for the large jeeps is 1,100,000 gallons per trip.
this is analogous to gallons per mile where trip is being used in place of miles with the assumption that they are talking about the same trip for both which means the same number of miles for both.
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total fuel available is given as 18,600,000 gallons.
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the implicit assumption in this problem is that the fleet has been given just the right amount of small jeeps and large jeeps so that the total number of gallons consumed by them will exactly equal the total number of gallons available.
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that's the only assumption i could make that made sense based on what was given.
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using that assumption, i did the following:
i assumed that the number of small jeeps times the number of gallons per trip + the number of large jeeps times the number of gallons per trip had to be equal to the total number of gallons available.
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the equation came out to be:
800,000 * S + 1,100,000 * L = 18,600,000
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since i know that S = 5/2 * L, i can susbtitute 5/2 * L for S in the equation to get:
800,000 * (5/2 * L) + 1,100,000 * L = 18,600,000
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L can be factored out on the left side of the equation to make it:
L * ((800,000 * 5/2) + 1,100,000)) = 18,600,000
simplify:
L * (2,000,000 + 1,100,000) = 18,600,000
L * (3,100,000) = 18,600,000
divide both sides of the equation by 3,100,000 to get:
L = 18,600,000 / 3,100,000
which becomes:
L = 6
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since L = 6, and S = 5/2 * L, then S must be:
5 * 6 / 2 = 5 * 3 = 15
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now i have:
S = 15
L = 6
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do these numbers hold up?
i test in the original formulas to see if they do.
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if S = 5/2 * L, then 15 must be equal to 5/2 * 6.
5/2 * 6 = 30 / 2 = 15.
15 is equal to 15 so that part of the answer holds up.
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S * 800,000 + L * 1,100,000 = 18,600,000
15 * 800,000 + 6 * 1,100,000 = 18,600,000
12,000,000 + 6,600,000 = 18,600,000
18,600,000 = 18,600,000
this equation holds up also so the answer must be correct based on the assumptions.
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the major assumption that i chose to work this problem is that the number of small jeeps and large jeeps were chosen based on the fact that their consumption rates would allow them to very conveniently consume just the right amount of fuel so that the total supply would be exhausted at the same time.
tht was implied by the problem statement because of the way the problem was presented although it wasn't explicitly stated. hopefully i made the right choice. if i did, then you have the right answer.
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