Chickens can lay eggs twice a day
Rule of three
Rule of three (multiple proportionality - second example)
One and a half chickens lay one and a half eggs in a day and a half. How many eggs does a chicken lay in a day?
First you write the numbers in a scheme:
|1,5||Lay chickens||1,5||Eggs in||1,5||Days|
|1||Chicken lays||Eggs on||1||Day|
It is important that the same sizes are placed on top of each other: chickens have to stand above chickens, eggs above eggs, days after days.
Since it only comes down to the numbers, you write the same scheme with only numbers:
The column with the is in the middle, so you don't need to rearrange the columns.
Next you determine whether the size in the middle column, here eggs, is directly proportional or inversely proportional to the other two sizes, i.e. chickens on the one hand and days on the other. Here the first ratio is directly proportional: the more Chicken, the more Eggs. The other ratio is also proportional: the more Days the more Eggs.
So you multiply both times crosswise. The product of the three numbers marked in yellow must be equal to the product of the three numbers marked in blue:
|Fig. 1: Multiplication with twice direct proportionality|
In this example, the following must apply:
1,5 · · 1,5 = 1 · 1,5 · 1 .
You can find the result, the number you are looking for, by solving the equation for:
You can shorten the fraction by 1.5 and then expand it by 2, the result is 2/3:
You express the solution in words in response to the question posed in the task:
"1 chicken lays 2/3 eggs in one day."
As a test, you take a very rough look to see whether the result can be correct. If you first look at the 1.5 day period, then 1.5 chickens will lay 1.5 eggs, so 1 chicken will lay 1 egg. If you now reduce the period by a third, the egg production must also decrease by a third. So the result of 2/3 eggs is correct!
This task was given to the participants at an international mathematics congress. The mathematicians' answers were:
- "I've had an eight hour flight behind me - I can't answer the question now."
- "An egg."
- "I'm sorry - that's not my area of expertise."
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