Algebra Word Problems and Constant of Variation

1. For a healthy flamingo, the length of the legs is directly proportional to the total height of the bird. A healthy flamingo, which is 48 inches tall, has legs that are 32 inches long.

a. Write a formula, using only variables, that could be used to determine the constant of variation.

b. Find the constant of variation k. Describe the steps required to arrive at your answer.

c. Suppose a researcher finds a flamingo that is 56 inches tall. Use your equation from part a and your solution from part b to determine how long its legs should be? Describe how you arrived at your answer.

2. Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are $2,500 for setup costs and $3.00 to administer each test.

a. Write an expression that gives the total cost to test x animals.

b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal.

c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals.

d. As the number of animals tested increases, what happens to the average cost to test the animals? Would the average cost ever fall below $3.00? If so, identify a value that supports your answer. If not, explain how you know.

e. How many animals should be tested for the average cost to be $5.00 per animal?

3. To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.

a. Write an equation using only one variable that could be used to solve for the constant of variation k.

b. A biologist counted the number of white tail deer in a 100 acre parcel of land in a nature preserve and found 12 deer. Find the constant of variation k.

c. If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve?