ACT Math : How to use the direct variation formula
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Example Questions
Example Question #1 : How To Use The Direct Variation Formula
The price of silver varies directly as the square of the mass. If 3.6 g of silver is worth $64.80, what is the value of 7.5 g of silver?
$178.50
$281.25
$215.25
$135.00
$301.75
$281.25
This is a direct variation problem of the form y = kx2 The first set of data 3.6 g and $64.80 is used to calculate the proportionality constant, k. So 64.80 = k(3.6)2 and solving the equation gives k = 5.
Now we move to the new data, 7.5 g and we get y = 5(7.5)2 to yield an answer of $218.25.
$135.00 is the answer obtained if using proportions. This is an error because it does not take into consideration the squared elements of the problem.
Example Question #1 : Direct And Inverse Variation
The diameter of a specific brand of candy wrapper is 
The question asks for an equation that can relate 
This gives us:
Example Question #1 : How To Use The Direct Variation Formula
An instrument reads two values, 
An instrument reads two values, 
Direct variation means that any pairing of the related values will always have the same ratio, thus we know that for any other values 
Thus, for our information, we know:
This means that the new values of 
Example Question #2 : Direct And Inverse Variation
In an experimental setting, the pressure and the temperature of gas in a container are directly proportional. In the first experiment, the pressure of the gas was 
It cannot be determined.
For direct variation of related variables, we know that the following equation holds:
For our data, this would be:
To start simplifying and solving this, first factor the top of the left fraction:
Cancel the 
Next, multiply by 
Since 
Simplify:
Example Question #3 : How To Use The Direct Variation Formula
In a given solution, the proportion of water to apple juice is directly proportional. If the first batch of the solution contained 
This problem is easily solved by setting up a ratio. For directly proportional amounts, we know:
For our data, this would be:
This is first simplified as being:
Next, multiply by 
Finally:
Example Question #2 : How To Use The Direct Variation Formula
The length, in inches, of a box is 
Since the question asks for the length in terms of width, I like to start by setting the problem up as 
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