Question

A farmer raises goats and cows. Each goat requires 400 square feet of grazing area and each cow requires

1,200 square feet of grazing area. The farmer has 36,000 square feet for grazing area. Write a function to
represent the combination of goats and cows that the farmer can raise. Let a represent the number of goats,
and y represent the number of cows.

Answer 1

The function representing the combination of goats and cows within the grazing area is a = 90 - 3y, where 'a' is the number of goats and 'y' is the number of cows. This considers each goat needing 400 square feet and each cow needing 1,200 square feet, with a total grazing area of 36,000 square feet.

Step-by-step explanation:

The question asks us to write a function to represent the combination of goats and cows that a farmer can raise based on the grazing area each animal requires. Each goat requires 400 square feet, and each cow requires 1,200 square feet of grazing area. The farmer has 36,000 square feet available for grazing. Let a represent the number of goats, and y represent the number of cows.

The function modeling the possible combinations of goats (a) and cows (y) is:

(400 × a) + (1,200 × y) = 36,000

This can be simplified to:

a + 3y = 90

So, the function expressing the relationship between the number of goats and cows a farmer can have based on the available grazing area is:

a = 90 - 3y