A chicken farmer has identified that a hen and also a half can lay an egg and also a fifty percent in a day and a half.How countless hens go the farmer need to produce one dozen eggs in 6 days?


This is a classic problem that many people get wrong since they reason that fifty percent of a hen cannot lay one egg, and also a hen cannot lay fifty percent an egg. However, us can gain a satisfactory equipment bytreating this together a completely mathematical trouble where the numbers represent averages.

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To resolve the problem, we very first need to discover the rate at i m sorry the hen lay eggs.The problem can be represented by the complying with equation, whereby RATEis the number of eggs produced per hen·day:1½ hen × 1½ days × rate = 1½ eggs

We convert this to fountain thus:3/2 hen × 3/2 job × rate = 3/2 eggsMultiplying both sides of the equation through 2/3, us get:1 hen × 3/2 days × rate = 1 eggMultiplying both sides of the equation again by 2/3 and also solving because that RATE, we get:RATE = 2/3 eggs per hen·dayNow that we know the price at which hen lay eggs, we can calculate how countless hens (H)can create 12 eggs in 6 days making use of the complying with equation:H hen × 6 job × 2/3 eggs every hen·day = 12 eggsSolving for H, us get:H = 12 eggs /(6 work × 2/3 eggs every hen·day) = 12/4 = 3 hensTherefore, the farmer requirements 3 hens to produce 12 eggs in 6 days.

Steve Salazar Jr. Sent out the adhering to comment:

Maybe a small chart will assist some of your readers understand "The Chicken and also Egg Problem".I likewise thought you to be wrong until I did this small chart.


notes hen eggs 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 work will dual the eggs, yet not the hens. 3 6 3
dual the days again (to with 6 days) will double the egg again, yet not the hens. 3 12 6


Reader Dan sent out the adhering to comment:

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

Unfortunately, Dan has actually made a mistake by multiplying everything by 2, thereby an altering the price of egg production. In the initial problem, the rate in eggs per hen·day is:

1.5 eggs rate = ——————————————————— = 2/3 eggs/hen·day 1.5 hens × 1.5 daysBy the rule of algebra, you deserve to multiply both the numerator and denominator through 2, i beg your pardon is the very same as multiply by one. So, you can dual the variety of eggs to 3 in the numerator, and, in the denominator, girlfriend can double the hens or double the days, yet you cannot double both. By multiplying everything by 2, Dan has actually really multiply the rate by 2/(2×2) or 1/2,changing the from 2/3 come 1/3.

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Reader Joshua asked:

Regarding the "Chicken and the Egg" problem,I was wondering if you might share v me why leader Dan"s mathematics is false?In her own occupational of the equation, I have noticed that you neglected tomultiply the days of the equation through 2/3 in your 2nd step. Have the right to you pleaseexplain come me why girlfriend neglected to do so?

Let me deal with the second question first. As soon as we main point the equation by 2/3, us have:

2/3×(3/2 hens × 3/2 work × RATE) = 2/3×(3/2 eggs)1 hen × 3/2 job × price = 1 eggBy the commutative regulations of algebra, over there is no difference between the equation above and: 3/2 hen × work × price = 1 egg
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The image above may clarification why leader Dan make a mistake. The multiplied whatever times two, doubling the moment period, and also doubling the number of hens. He interpreted this to average thatthree hens will lay 3 eggs in 3 days, and therefore the one hen lays one egg every day, i beg your pardon is wrong.The correct postulation the the difficulty is shown below where a hen and fifty percent lays one egg and also a fifty percent in a day and also a half,and through doubling the moment period, this very same hen and a half lays 3 egg in 3 days. This offers a rate:


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Domestication of chickens take it place much more than 8,000 years ago in what is now Thailand and also Vietnam, the region in i m sorry red junglefowl are discovered today. Chicken bones dating to around 7,500 years earlier have been uncovered at Neolithic sites in ~ the mouth of the Yellow river in China. Evidence of chicken domestication 4,000 years back has likewise been uncovered in Pakistan.