5/10/21 Inverse Variation Word Problems

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables in which the product of the variables is constant. If one variable increases, the other decreases.

Front

If length (L) is inversely proportional to width (W), what is the relationship expressed mathematically?

Back

L * W = k, where k is a constant.

Front

Given L = 25 and W = 3, find the constant k.

Back

k = L * W = 25 * 3 = 75.

Front

If L = 5, what is W when k = 75?

Back

W = k / L = 75 / 5 = 15.

Front

In a limo rental scenario, if the number of people (P) varies inversely with the cost per person (C), what is the relationship?

Back

P * C = k, where k is a constant.

Front

If 6 people cost $48 per person, what is the constant k?

Back

k = 6 * 48 = 288.

Front

If the number of people changes to 12, what is the new cost per person?

Back

C = k / P = 288 / 12 = $24.

Front

In kickboxing, if force (f) varies inversely with length (l), what is the relationship?

Back

f * l = k, where k is a constant.

Front

If it takes 15 lbs of pressure to break a 4-foot board, what is k?

Back

k = 15 * 4 = 60.

Front

How many pounds of pressure are needed to break a 10-foot board?

Back

f = k / l = 60 / 10 = 6 lbs.