The school cook has ordered 37 trays of a dozen eggs. How many eggs has she ordered?
Answers
Answer:
We solve this problem by turning the question into two equations. (When the question was set in ancient China they were not able to do this since this technique had not yet been invented. And perhaps this is why there are, in fact, four solutions.)
If the number of cocks, hens and chicks are x, y and z. Then we have
(A) x + y + z = 100
(B) 5x + 3y + z/3 = 100
Multiply (B) by 3 to get (C) 15x + 9y + z = 300. From (A) we know that z = 100 – x – y. Substitute that expression for the z in (C) and we get an equation that simplifies to 14x + 8y = 200. We can assume from the question that since we are dealing in animals, we cannot buy fractions of animals. In other words we are looking for whole number solutions, and the only way to find them is trial and error. There are four solutions
- x = 0 and y = 25, in which case z = 75
- x = 4 and y = 18, in which case z = 78
- x = 8 and y = 11, in which case z = 81
- x = 12 and y = 4, in which case z = 84
The answer is that you would buy either zero cocks, 25 hens and 75 chicks, OR 4 cocks, 18 hens and 78 chicks, OR 8 cocks, 14 hens and 78 chicks, OR 12 cocks, 4 hens and 84 chicks.