Algebra II : Algebra II
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #22 : Equations / Solution Sets
We have three cats, Chai, Sora, and Newton. Chai is 3 years old. Sora two years older than twice Chai's age. Newton is one year younger than one-fourth of Sora's age. How old are Sora and Newton?
Sora: 8 years
Newton: 1 year
Sora: 4 years
Newton: one half year
Sora: 5 years
Newton: 6 years
Sora: 1 year
Newton: 8 years
Sora: 3 years
Newton: not born yet
Sora: 8 years
Newton: 1 year
To make this much easier, translate the word problem into a system of three equations.
We have C for Chai, S for Sora, and N for Newton. To find Sora's age, plug in 
Sora is 8 years old. Use this to find Newton's age.
Newton is one year old. So the answer is:
Sora, 8 years
Newton, 1 year
Example Question #1 : How To Find The Missing Number In A Set
The sum of three consecutive even integers equals 72. What is the product of these integers?
13728
17472
10560
13800
12144
13728
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
Example Question #1 : Setting Up Expressions
Express as a mathematical expression.
Take every word and translate into math.
That something is 
Example Question #1 : Expressions
Express as a mathematical expression.
Take every word and translate into math.
That something is 
Example Question #7 : Setting Up Expressions
Express as a mathematical expression.
Take every word and translate into math.
That something is 
Example Question #3 : Setting Up Expressions
Express as a mathematical expression.
The quotient of 
Take every word and translate it into math.
Anytime you take a quotient of 
Therefore expression is
Example Question #11 : Setting Up Expressions
Express as a mathematical expression.
Take every word and translate it into math.
That something is 
Example Question #1892 : Algebra Ii
Express as a mathematical expression.
Take every word and translate into math.
Anytime you take a quotient of 
Let's combine to create the expression of 
Example Question #11 : Expressions
Jacob just opened a soda bottling factory. His starting costs were 
The $10,000 that Jacob invested can be considered as a negative starting value, which will be the y-intercept in the equation.
The total money Jacob makes depends on how many bottles he sells.
If each bottle earns Jacob 50 cents, then the correct equation is 
Example Question #1894 : Algebra Ii
Lisa has $6. She wants to buy some apples and bananas, but wants exactly ten fruits total. If bananas cost 50 cents each and apples cost $1 each, how many apples and bananas should she get?
Let 
We need to write two equations, one for the total cost of all the fruits, and one for the total number of fruits.
If 
For the other equation we know the price of each fruit and the total amount she wants to spend.
We have now identified the two equations. If you were to solve them, you would see that 
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