Question

a farmer notes that in a field of goats and geese there are 41 heads and 114 feet how many of each animal are there

Answer 1

There are 25 geese and 16 goats

Explanation:

Let O represent the # of goats and E the # of geese. Remembering that goats have four feet and geese only two, and that each animal has only one head, we can write the following equations to determine O and E:

Number of heads: 41; this is the total of the # of goat heads and the # of goose heads: O + E = 41

(4 feet per goat)O + (2 feet per goose)E = 114 (There are a total of 114 feet)

Then we solve the following system of linear equations:

O + E = 41

4O + 2E = 114

Multiplying the first equation by -2 results in -2O - 2E = -82.

Combining this result with the second equation, we obtain the system

4O + 2E = 114

-2O - 2E = -82

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2O = 32

Then O = # of goats = 32/2, or 16, and so the equation O + E = 41 becomes

E = # of geese = 41 - O (remembering that we found O to be 16), or

E = 41 - 16 = 25

There are 25 geese and 16 goats.