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Help: average problem

by praveen_gmat » Fri Aug 27, 2010 1:13 am
Two different chicken coops, Coop A and Coop B, contain only Leghorn and Marans chickens. A Leghorn chicken lays a certain average number of eggs per month, and a Marans chicken lays a certain average number of eggs per month. Coop A houses 10 Leghorn chickens and 8 Marans chickens and produces an average of 440 eggs in a month. Coop B houses 7 Leghorn chickens and 4 Marans chickens and produces an average of 280 eggs in a month. On average, how many more eggs per month does a Leghorn chicken lay than a Marans chicken?
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by limestone » Fri Aug 27, 2010 2:06 am
Let's call the average no. of eggs that a Leghorn lays a month is "x"
"y" is that of Marans
From Coop A : 10x +8y = 440
From Coop B: 7x + 4y = 280, or we can say 14x + 8y = 560 ( multiply both sides to 2)
(14x + 8y) - (10x + 8y) = 560 -440
4x =120 or x =30
7x + 4y = 280, while x =30, then 7*30 + 4y = 280
4y =70, y = 17.5
x-y = 30-17.5 = 12.5
So 12.5 is No. of eggs per month a Leghorn chicken lays more than a Marans chicken.
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by praveen_gmat » Fri Aug 27, 2010 2:08 am
limestone wrote:Let's call the average no. of eggs that a Leghorn lays a month is "x"
"y" is that of Marans
From Coop A : 10x +8y = 440
From Coop B: 7x + 4y = 280, or we can say 14x + 8y = 560 ( multiply both sides to 2)
(14x + 8y) - (10x + 8y) = 560 -440
4x =120 or x =30
7x + 4y = 280, while x =30, then 7*30 + 4y = 280
4y =70, y = 17.5
x-y = 30-17.5 = 12.5
So 12.5 is No. of eggs per month a Leghorn chicken lays more than a Marans chicken.
Yeah you are right ..
You know what I did .. :(


10L + 8M
-------------- = 440 .... which implies that 5L + 4M = 3960
18


7L + 4M
------------- = 280 ....... which implies that 7L + 4M = 3080
11



This will give negative values ..
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by gmatmachoman » Fri Aug 27, 2010 2:49 am
limestone wrote:Let's call the average no. of eggs that a Leghorn lays a month is "x"
"y" is that of Marans
From Coop A : 10x +8y = 440
From Coop B: 7x + 4y = 280, or we can say 14x + 8y = 560 ( multiply both sides to 2)
(14x + 8y) - (10x + 8y) = 560 -440
4x =120 or x =30
7x + 4y = 280, while x =30, then 7*30 + 4y = 280
4y =70, y = 17.5
x-y = 30-17.5 = 12.5
So 12.5 is No. of eggs per month a Leghorn chicken lays more than a Marans chicken.
dude, i should admit i got this the way u did, but was bit wary how come eggs be in decimals..so hunned away from posting..

anyways good prblm...
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by praveen_gmat » Fri Aug 27, 2010 2:50 am
gmatmachoman wrote:
limestone wrote:Let's call the average no. of eggs that a Leghorn lays a month is "x"
"y" is that of Marans
From Coop A : 10x +8y = 440
From Coop B: 7x + 4y = 280, or we can say 14x + 8y = 560 ( multiply both sides to 2)
(14x + 8y) - (10x + 8y) = 560 -440
4x =120 or x =30
7x + 4y = 280, while x =30, then 7*30 + 4y = 280
4y =70, y = 17.5
x-y = 30-17.5 = 12.5
So 12.5 is No. of eggs per month a Leghorn chicken lays more than a Marans chicken.
dude, i should admit i got this the way u did, but was bit wary how come eggs be in decimals..so hunned away from posting..

anyways good prblm...
@gmatmachoman

Yeah mate .. I think the problem is ridiculously stupid. :D
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by limestone » Fri Aug 27, 2010 5:08 am
The author is talking about the average no. of eggs that those chicken lay per month. So take an example:
First month, 1 Leghorn laid 13 eggs. Second month, 12 eggs. Third, 14 and forth 11.
Average eggs laid per month = (13+12+14+11)/4 = 12.5

That's it!!
Hope this could help.
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by sdotcruz » Fri Aug 27, 2010 6:20 am
limestone,

Why do we ignore the average formula in this problem? Are there some key words in the problem that lead us to the straight algebraic equation?
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by limestone » Fri Aug 27, 2010 7:12 am
Two different chicken coops, Coop A and Coop B, contain only Leghorn and Marans chickens. A Leghorn chicken lays a certain average number of eggs per month, and a Marans chicken lays a certain average number of eggs per month. Coop A houses 10 Leghorn chickens and 8 Marans chickens and produces an average of 440 eggs in a month. Coop B houses 7 Leghorn chickens and 4 Marans chickens and produces an average of 280 eggs in a month. On average, how many more eggs per month does a Leghorn chicken lay than a Marans chicken?
The question gives us a confusing word: average. I'll take an example:
1 Leghorn lays average 15 eggs per month ( some months It lays 12, some it lays 16 or even 20, but the average eggs laid of all these months is 15, then the average formula is here)
So 2 Leghorns lay how many eggs on average per month? (15+15)/2 ? Not that way. It must be 15 *2 = 30
So 2 Leghorns & 1 Marans lay how many eggs on average per month? 15*2 + 10 ( 10 is the eggs laid by Maran on average per month)
Thus 10 Leghorns and 8 Marans lay: 10 * x + 8 * y , with x is the no. of eggs laid by one Leghorn on average per month, and y is that of Maran. We got 10x + 8y =440
And 7x +4y =280
Is it clear now?
Anyway, is it odd that an average chick can lay 440 eggs per month, or nearly 15 eggs per day?
Hope it help
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