All Algebra II Resources
Example Questions
Example Question #1 :Proportionalities
Sarah notices her map has a scale of. She measuresbetween Beaver Falls and Chipmonk Cove. How far apart are the cities?
is the same as
So to find out the distance between the cities
Example Question #1 :How To Find Direct Variation
如果一个对象是挂在一个春天,伸长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?
Letbe the mass of the weight and the elongation of the spring. Then for some constant of variation,
We can findby settingfrom the first situation:
so
In the second situation, we setand solve for:
which rounds to 11.5 centimeters.
Example Question #1 :Understanding Direct Proportionality
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 #1 :Proportionalities
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 #2 :Proportionalities
Findfor the proportion.
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 distance between New York City and Los Angeles in real life is, how far would the two cities be on Mark's map?
If the real distance between the two cities is, and=, then we can set up the proportional equation:
Example Question #7 :Basic Single Variable Algebra
Ifand, findand.
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. We therefore get:
With our, we can now find x using the first equation:
We therefore get the correct answer ofand.
Example Question #8 :Basic Single Variable Algebra
如果一个对象是挂在一个春天,伸长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?
Letbe the mass of the weight and the elongation of the spring, respectively. Then for some constant of variation,
.
We can findby setting:
Therefore.
Setand solve for:
kilograms
Example Question #1 :How To Find Direct Variation
Ifis directly proportional toand whenat, what is the value of the constant of proportionality?
The general formula for direct proportionality is
whereis the proportionality constant. To find the value of this, we plug inand
Solve forby dividing both sides by 12
So.
Example Question #1 :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
whereis how much money you earned,is the proportionality constant, andis the number of hours worked.
Before we can figure out how many hours you need to work to earn $48, we need to find the value of. It is given that you earned $32 by working 4 hours. Plug these values into the formula
Solve forby dividing both sides by 4.
So. We can use this to find out the hours you need to work to earn $48. With, we have
Plug in $48.
Divide both sides by 8
So you will need to work 6 hours to earn $48.