A chicken farmer has established that a hen and a half can put an egg and a half in a day and a half.How many hens walk the farmer require to develop one dozen egg in six days?

This is a standard problem that many world get wrong due to the fact that they factor that fifty percent of a hen cannot lay an egg, and also a hen cannot lay half an egg. However, we can get a satisfactory solution bytreating this as a completely mathematical trouble where the numbers represent averages.

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To fix the problem, we first need to find the price at which the hen lay eggs.The problem can be represented by the complying with equation, wherein RATEis the number of eggs developed per hen·day:1½ hen × 1½ days × rate = 1½ eggs

We transform this to fractions thus:3/2 hens × 3/2 days × rate = 3/2 eggsMultiplying both political parties of the equation by 2/3, us get:1 hen × 3/2 days × price = 1 eggMultiplying both political parties of the equation again by 2/3 and also solving for RATE, us get:RATE = 2/3 eggs per hen·dayNow that we know the rate at which hens lay eggs, we can calculate how many hens (H)can create 12 egg in 6 days utilizing the following equation:H hens × 6 work × 2/3 eggs per hen·day = 12 eggsSolving because that H, we get:H = 12 egg /(6 work × 2/3 eggs per hen·day) = 12/4 = 3 hensTherefore, the farmer demands 3 hens to develop 12 eggs in 6 days.

Steve Salazar Jr. Sent out the adhering to comment:

Maybe a tiny chart will help some of her readers recognize "The Chicken and Egg Problem".I additionally thought you to be wrong until I go this little chart.

notes hens egg days
1.5 eggs/1.5 hens/1.5 job 1.5 1.5 1.5
doubling the hens will double the eggs, however not the days. 3 3 1.5
then doubling the job will twin the eggs, however not the hens. 3 6 3
dual the job again (to reach 6 days) will twin the eggs again, but not the hens. 3 12 6

Reader Dan sent the adhering to comment:

I think her answer is wrong for The Chicken and also Egg Problem.After a pack of overcomplex calculations you arrive at the dorn answerof "Therefore, the farmer needs 3 hen to create 12 eggs in 6 days."The exactly answer is 2.A hen and a fifty percent can put an egg and also a fifty percent in a day and also a fifty percent = 1 hen lays 1 egg per day. To simplify it, just dual it:3 hen lay 3 eggs in 3 job = 1 hen lays 1 egg in 1 day.So 2 hens lay 12 egg in 6 days.

Unfortunately, Dan has made a wrong by multiplying every little thing by 2, thereby changing the price of egg production. In the initial problem, the price in eggs per hen·day is:

1.5 eggs rate = ——————————————————— = 2/3 eggs/hen·day 1.5 hens × 1.5 daysBy the rules of algebra, you deserve to multiply both the numerator and denominator by 2, which is the exact same as multiply by one. So, friend can twin the variety of eggs to 3 in the numerator, and, in the denominator, you can double the hen or dual the days, however you cannot twin both. By multiplying everything by 2, Dan has actually really multiplied the price by 2/(2×2) or 1/2,changing the from 2/3 to 1/3.

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Reader Joshua asked:

Regarding the "Chicken and also the Egg" problem,I was wondering if you can share v me why reader Dan"s mathematics is false?In her own job-related of the equation, I have noticed the you neglected tomultiply the work of the equation by 2/3 in your 2nd step. Have the right to you pleaseexplain come me why you neglected to execute so?

Let me resolve the 2nd question first. Once we main point the equation through 2/3, we have:

2/3×(3/2 hens × 3/2 days × RATE) = 2/3×(3/2 eggs)1 hen × 3/2 days × price = 1 eggBy the commutative legislations of algebra, over there is no difference between the equation above and: 3/2 hen × work × price = 1 egg

The image above may clear up why leader Dan do a mistake. He multiplied whatever times two, doubling the moment period, and also doubling the number of hens. He taken this to mean thatthree hens will lay three eggs in 3 days, and also therefore the one hen lays one egg per day, i beg your pardon is wrong.The exactly postulation that the difficulty is shown below where a hen and half lays one egg and a fifty percent in a day and a half,and by doubling the time period, this very same hen and a half lays 3 egg in 3 days. This provides a rate:


Domestication of chickens took place much more than 8,000 years ago in what is now Thailand and also Vietnam, the region in i beg your pardon red junglefowl are discovered today. Chicken bones dating to about 7,500 years back have been discovered at Neolithic sites at the mouth the the Yellow river in China. Proof of chicken domestication 4,000 years back has also been uncovered in Pakistan.