A man has a 100-acre ranch that he wishes to stock with cows and sheep. Cows require ten acres of grazing land per animal and sheep require three acres of grazing land per animal. If he wishes to fully utilize the land, how many ways are there to stock the ranch so that it includes at least one cow and at least one sheep?

3 ways

Step-by-step explanation:

From the question:

Number of acres of the land = 100 acres

1 cow = 10 acres of land

1 sheep = 3 acres of land

To fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is calculated as:

1) 1 cow and 30 sheep

1 cow × 10 acres + 30 sheep × 3 acres

10 + 90 = 100 acres

2) 4 cows and 20 sheep

4 cow × 10 acres + 20 sheep × 3 acres

40 + 60 = 100 acres

3) 7 cows and 10 sheep

7 cow × 10 acres + 10 sheep × 3 acres

70 + 30 = 100 acres

Therefore, to fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is 3 ways

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