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Algebra I: Variation

Problems

Inverse Variation

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Problem : Could the relationship between the following quantities be represented by an inverse variation equation?
a) The rate of travel and the time needed to travel a certain distance.
b) The number of pages you read in a book and the number of pages you have left to read.
c) The rate of travel and the total distance traveled.
d) The number of children present and the number of cookies each can have if a box of cookies is divided evenly.

a) Yes.
b) No, the sum of the two quantities, not the product, is constant.
c) No, this is a direct variation equation.
d) Yes.

Problem : In parts (a) and (d) in the previous problem, what does the constant k represent?

a) The total distance to be traveled
b) The total number of cookies in the box

Problem : If y varies inversely as x , and y = 6 when x = 5, write an equation describing the variation.

xy = 30

Problem : If y varies inversely as x , and the constant of variation is 75, what is y when x = 12.5 ?

y = 6

Problem : If h varies inversely as k , and the constant of variation is , what is k when h = 6 ?

k =

Problem : If y varies inversely as x , and y = 7 when x = 6 , what is y when x = 3 ? What is x when y = 3 ?

y = 14
x = 14 .

Problem : If y varies inversely as x , and y = 6 when x = 3a , what is y when x = a ?

y = 18

Problem : If y varies inversely as x , and y = 4b when x = 6a , what is y in terms of a and b when x = 8 ?

y = 3ab

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