In this lesson, we will learn how to solve direct proportions (variations) and inverse proportions (inverse variations) problems. (Note: Some texts may refer to inverse proportions/variations as indirect proportions/variations.)
Two values x and y are directly proportional to each other when the ratio x : y or is a constant (i.e. always remains the same). This would mean that x and y will either increase together or decrease together by an amount that would not change the ratio.
Knowing that the ratio does not change allows you to form an equation to find the value of an unknown variable, for example:
If two pencils cost $1.50, how many pencils can you buy with $9.00?
The number of pencils is directly proportional to the cost.
This video shows how to solve direct proportion questions
Example 1: F is directly proportional to x. When F is 6, x is 4. Find the value of F when x is 5.
Example 2: A is directly proportional to the square of B. When A is 10, B is 2. Find the value of A when B is 3.
Two values x and y are inversely proportional to each other when their product xy is a constant (always remains the same). This means that when x increases y will decrease, and vice versa, by an amount such that xy remains the same.
Knowing that the product does not change also allows you to form an equation to find the value of an unknown variable for example:
It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate?
The number of men is inversely proportional to the time taken to do the job.
Usually, you will be able to decide from the question whether the values are
directly proportional or inversely proportional.
How to solve inverse proportion questions.
This video shows how to solve inverse proportion questions. It goes through a couple of examples and ends with some practice questions
Example 1: A is inversely proportional to B. When A is 10, B is 2. Find the value of A when B is 8
Example 2: F is inversely proportional to the square of x. When A is 20, B is 3. Find the value of F when x is 5.
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