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John.s car dealership contains m cars, 20% of which are
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26 Feb 2012, 16:17
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John.s car dealership contains m cars, 20% of which are minivans and 80% are sedans. Kevin's car dealership contains n cars, 40% of which are minivans are 60% are trucks. Larry's car dealership contains p cars, 50% of which are minivans and 50% of which are convertibles. If 25% of the m + n + p cars contained at the three dealerships are minivans, what is m in terms of n and p?
Ok I tried doing this this question in 2 ways. 1----> By picking numbers for m, n and p and I struggled to get the right answer and I need help. 2-----------> Algebraically and I got the correct answer.
So Method 1 (Number picking)
John Dealership Let say m = 200 Minivans = 20 ----------------------> I will only talk about Minivan's as the question is about minivans.
Kevin dealership Let say n = 300 Minivans = 40
Larry dealership let say n = 300 Minivan's = 50
Total cars at the dealership = 600 Minivans = 150 -------------------------------(25% of 600)
After this I struggled.............can someone please help?
MY algebraic approach
0.2m + 0.4n + 0.5p = 0.25m + 0.25n + 0.25p
Solving for m will give m = 3n + 5p which is the right answer.
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Re: John.s car dealership contains m cars, 20% of which are
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26 Feb 2012, 17:54
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John.s car dealership contains m cars, 20% of which are minivans and 80% are sedans. Kevin's car dealership contains n cars, 40% of which are minivans are 60% are trucks. Larry's car dealership contains p cars, 50% of which are minivans and 50% of which are convertibles. If 25% of the m + n + p cars contained at the three dealerships are minivans, what is m in terms of n and p? (A) n + 3p (B) 3n + 5p (C) 4n + 5p (D) (n+5p)/2 (E) (4n+5p)/3
For this question algebraic ways is the easiest: \(0.2m+0.4n+0.5p=0.25(m + n + p)\) --> \(m=3n+5p\).
Answer: B.
enigma123 wrote:
John Dealership Let say m = 200 Minivans = 20 ----------------------> I will only talk about Minivan's as the question is about minivans.
Kevin dealership Let say n = 300 Minivans = 40
Larry dealership let say n = 300 Minivan's = 50
Total cars at the dealership = 600 Minivans = 150 -------------------------------(25% of 600)
After this I struggled.............can someone please help?
First of all you have miscalculated # of minivans and total cars: 20% of 200 = 40; 40% of 300 = 120; 50% of 300 = 150; Total minivans = 310; Total cars = 800.
But this is not the main problem: you can not arbitrary assign numbers to m, n and p here. Because 0.2m+0.4n+0.5p must equal to 0.25(m + n + p). For your numbers 25% of (m + n + p)=800 is 200 and not 310.
To summarize this is not a good problem for number plugging.
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gmatclubot
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