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For example, if we say "," we are faced with combined variation. Assuming that each person is capable of painting at the same rate, how long will it take for 12 people to paint 1,800 ft. This can be written as follows: Consider the following example: It takes 2 hours for 3 people to paint 100 ft.
Two ratios are said to be equal if, when written in fractional form, the fractions are equivalent fractions.
You can compare and solve ratios using cross multiplications.
Let’s take a look at an example of direct variation.
The amount of flour needed in a bread recipe varies with the number of loaves being made.
Problems involving direct variation can be solved using proportions.
Let’s see this in action: If it takes 3 gallons of paint to cover 100 square feet, how many gallons of paint will be needed to cover 600 square feet?
Joint variation is just an extension of direct variation.
When we say that " is 8) into our joint variation equation: Once we have a value forwe plug this back into the equation of joint variation along with the variables we do know and solve for our unknown: Combined variation involves both direct and inverse variation. (Note, we are using different letters for our variables, but it doesn’t matter! The steps are the same as in the other example problems.
In this example, the time required to paint the house varies inversely with the number of people painting.
This means the more people painting the house, the less total time it will take to paint.