Question

A new species of wolf was just introduced into an environment that already contained rabbits and foxes. The wolves are better hunters, but there are fewer of them. Each wolf catches an average of 1.8 rabbits per day, while each fox only catches an average of 1.6 rabbits per day. Yet there are three times as many foxes as wolves. The rabbit population began at 13,800. Fifteen days later, that population has dropped to only 12,150. How many foxes are in the environment? How many wolves?

Answer 1

The total number of rabbits caught per day by wolves and foxes is equal to the decrease in the rabbit population over 15 days

• 1.8W + 1.6F = 13,800 - 12,150
• 1.8W + 1.6F = 1,650 (Equation 1)

The total number of rabbits caught per day by wolves and foxes is also equal to the total rabbit population decrease over 15 days:

• 15(1.8W + 1.6F) = 13,800 - 12,150
• 27W + 24F = 1,650 (Equation 2)

There are three times as many foxes as wolves

• F = 3W (Equation 3)

SOLUTION

• F = 3W

1.8W + 1.6(3W) = 1,650

1.8W + 4.8W = 1,650

6.6W = 1,650

W = 1,650 / 6.6

W = 250

F = 3W

F = 3(250)

F = 750

ANSWER

250 WOLVES AND 750 FOXES