At the Farmer’s Meat Market, Theo will sell you a certain number of geese for $27. Four more chickens than that cost $42. Six chickens and two geese will cost you $45. How much would you have to pay for one chicken? How much for one goose?
Let n be the “certain number” of geese that cost $27, g be the price of a goose, and c be the price of a chicken. (We quail at the large number of variables, but there are no quails in this problem, so we proceed bravely.)
- ng = $27, or g =
- (n + 4)c = $42, or c =
- 2g + 6c = $45.
We get everything in terms of n by substituting for g and c in (3), using (1) and (2):
Clearing of fractions, we get:
Putting in standard quadratic form, we have:
or n = 4.
In this context, n = 4, so g = 27/4 = 6.75. Substituting the value of g into (3), we find c = 5.25.
Thus a goose costs $6.75 and a chicken costs $5.25.