A chicken farmer has identified that a hen and also a fifty percent can place an egg and also a half in a day and a half.How many hens walk the farmer require to create one dozen eggs in six days?

This is a standard problem that many people get wrong because they reason that half of a hen can not lay an egg, and also a hen can not lay fifty percent an egg. However, us can acquire a satisfactory solution bytreating this together a completely mathematical problem where the numbers represent averages.

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To deal with the problem, we first need to uncover the price at i m sorry the hens lay eggs.The problem can be stood for by the complying with equation, wherein RATEis the variety of eggs created per hen·day:1½ hen × 1½ days × price = 1½ eggs

We convert this to fractions thus:3/2 hen × 3/2 days × price = 3/2 eggsMultiplying both political parties of the equation by 2/3, we get:1 hen × 3/2 work × rate = 1 eggMultiplying both political parties of the equation again through 2/3 and also solving because that RATE, us get:RATE = 2/3 eggs per hen·dayNow the we understand the rate at which hens lay eggs, we can calculate how countless hens (H)can create 12 egg in 6 days making use of the following equation:H hens × 6 job × 2/3 eggs every hen·day = 12 eggsSolving because that H, us get:H = 12 eggs /(6 days × 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 tiny chart will help some of her readers know "The Chicken and Egg Problem".I likewise thought you were wrong until I go this tiny chart.

 notes hen egg job 1.5 eggs/1.5 hens/1.5 days 1.5 1.5 1.5 copy the hens will twin the eggs, yet not the days. 3 3 1.5 climate doubling the work will dual the eggs, but not the hens. 3 6 3 dual the days again (to with 6 days) will dual the eggs again, however not the hens. 3 12 6

Reader Dan sent out the following comment:

I think her answer is wrong because that The Chicken and Egg Problem.After a load of overcomplex calculations you arrive 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 a fifty percent = 1 hen lays 1 egg per day. To leveling it, just dual it:3 hen lay 3 egg in 3 days = 1 hen lays 1 egg in 1 day.So 2 hens lay 12 eggs in 6 days.

Unfortunately, Dan has actually made a wrong by multiplying everything by 2, thereby transforming the rate 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 can multiply both the numerator and also denominator through 2, i beg your pardon is the exact same as multiply by one. So, girlfriend can twin the variety of eggs come 3 in the numerator, and, in the denominator, friend can twin the hen or twin the days, but you cannot double both. By multiplying everything by 2, Dan has actually really multiplied the rate by 2/(2×2) or 1/2,changing that from 2/3 to 1/3.

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