Farmers' Market, Chickens, Geese

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.)

1. ng = $27, or g =
2. (n + 4)c = $42, or c =
3. 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:

5n² - 14n - 24 = 0 → (5n + 6)(n - 4) = 0 → n = 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.