Problem Solving

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?

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.

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 ..

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 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.

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.

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?

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