Algebra II : Direct Proportionality
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #1 : Proportionalities
Sarah notices her map has a scale of 
So to find out the distance between the cities
Example Question #1 : How To Find Direct Variation
If an object is hung on a spring, the elongation of the spring varies directly as the mass of the object. A 20 kg object increases the length of a spring by exactly 7.2 cm. To the nearest tenth of a centimeter, by how much does a 32 kg object increase the length of the same spring?
Let 
We can find 
so
In the second situation, we set 
which rounds to 11.5 centimeters.
Example Question #2 : Proportionalities
Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?
(1 gallon = 4 quarts)
First set up the proportion:
x =
Then convert this to gallons:
Example Question #2 : Basic Single Variable Algebra
Sally currently has 192 books. Three months ago, she had 160 books. By what percentage did her book collection increase over the past three months?
To find the percentage increase, divide the number of new books by the original amount of books:
She has 32 additional new books; she originally had 160.
Example Question #1 : Direct Proportionality
Find 
To find x we need to find the direct proportion. In order to do this we need to cross multiply and divide.
From here we mulitply 100 and 1 together. This gets us 100 and now we divide 100 by 4 which results in
Example Question #6 : Basic Single Variable Algebra
On a map of the United States, Mark notices a scale of 
If the real distance between the two cities is 
Example Question #4 : Basic Single Variable Algebra
If 
We cannot solve the first equation until we know at least one of the variables, so let's solve the second equation first to solve for 
With our 
We therefore get the correct answer of 
Example Question #2 : How To Find Direct Variation
If an object is hung on a spring, the elongation of the spring varies directly with the mass of the object. A 33 kilogram object increases the length of a spring by exactly 6.6 centimeters. To the nearest tenth of a kilogram, how much mass must an object posess to increase the length of that same spring by exactly 10 centimeters?
Let 
We can find 
Therefore 
Set 
Example Question #4 : How To Find Direct Variation
If 
The general formula for direct proportionality is
where 
Solve for 
So 
Example Question #5 : How To Find Direct Variation
The amount of money you earn is directly proportional to the nunber of hours you worked. On the first day, you earned $32 by working 4 hours. On the second day, how many hours do you need to work to earn $48.
The general formula for direct proportionality is
where 
Before we can figure out how many hours you need to work to earn $48, we need to find the value of 
Solve for 
So 
Plug in $48.
Divide both sides by 8
So you will need to work 6 hours to earn $48.
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