Question

Formulate the situation as a system of inequalities. (Let x represent the number of goats the farmer can raise and y represent the number of llamas.) A rancher raises goats and llamas on his 800-acre ranch. Each goat needs 4 acres of land and requires $110 of veterinary care per year, while each llama needs 10 acres of land and requires $88 of veterinary care per year. If the rancher can afford no more than $14,520 for veterinary care this year, how many of each animal can he raise?

Answer 1

Answer: He can raise up to 40 goats and 100 llamas.

Explanation:

Hi, to answer this question we have to write system of equations with the information given:

The space each goat needs (4) multiplied by the number of goats (x); plus The space each llama needs (10) multiplied by the number of llamas must be less or equal to the acre land available (800)

4x +10y ≤ 800 (acres)

The amount of veterinary care (in $) each goat needs (110) multiplied by the number of goats (x); plus The amount of veterinary care each llama needs (88) multiplied by the number of llamas (y)must be less or equal to the Rancher's budget.(14520)

110x +88y ≤ 14,520 (cost)

Multiplying the first equation by 27.5, and subtracting the second equation to the first one:

110x + 275y ≤22,000

-

110x +88y ≤ 14,520

____________

187y ≤ 7480

y ≤ 7480/187

y ≤ 40

Replacing y in the first equation

4x +10(40) ≤ 800

4x +400 ≤ 800

4x ≤ 800-400

4x ≤ 400

x ≤ 400/4

x ≤ 100