Equations and Sequences

Question

Gaston claims to eat 6 dozen eggs every morning. If the hens in his town lay 2 eggs per day, what is equation that represents the relationship between the total number of eggs Gaston eats each morning and the number of hens (h) needed to support his diet?

Answer 1

This is a trick question. If there is a linear relation between the number of eggs Gaston Eats (Y) and the average productivity of a Hen (eggs per day/#hens) that relationship will be Y= a + bX..

We now that when X= 2 Y= 64. There are an infinite number of combinations of a and b that will ensure this. For instance b could be zero and a = 64. That way Gaston would Eat 64 eggs when X =1, X=2 or X=3. Another solution might be Gaston eats 32 + 16X. so when X=1 He eats 48 eggs and when X=2 he eats 64. To determine the two parameters of a linear relationship you need 2 observation.. Note that with two observation you can determine the productivity of the hens. You cannot determine the number of hens. To determine the number of hens you would need a third observation. The proportion of total eggs Gaston eats as a percentage of total eggs produced.

Hope this helps.

Lenny

Answer 2

6*12=2h.............