Algebra II : Setting Up Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #51 : Basic Single Variable Algebra

Express as a mathematical expression. 

 more than  times 

Possible Answers:

Correct answer:

Explanation:

Take every word and translate it into math. 

 more than means that you need to add  to something. 

 times something means that you need to multiply  to something.

That something is  so just combine them to have an expression of .

Example Question #52 : Basic Single Variable Algebra

Express as a mathematical expression. 

 is less than the quotient of  and 

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. 

 less than means that you need to subtract  from something.  

Anytime you take a quotient of  and  is the in the numerator and  is in the denominator. Therefore expression is .

Let's combine to create the expression of 

Example Question #11 : Expressions

Jacob just opened a soda bottling factory. His starting costs were . For each soda he bottles, he will make . Which of the following expressions shows how much money  Jacob will make in terms of , the number of sodas he bottles.

Possible Answers:

Correct answer:

Explanation:

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 #54 : Basic Single Variable Algebra

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  represent bananas and  represent apples. Set up the system of two equations but do not solve them.

Possible Answers:

Correct answer:

Explanation:

We need to write two equations, one for the total cost of all the fruits, and one for the total number of fruits.

If  represents the number of bananas, and  represents the number of apples, then from the problem statement we know that 

 must be equal to  because Lisa wants  total fruits.

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  and , so she should get  apples and  bananas.

Example Question #55 : Basic Single Variable Algebra

Set up the following expression:  Twenty less than eight times a number.

Possible Answers:

Correct answer:

Explanation:

To set up the expression, evaluate part by part.  Let  be the unknown number.

Eight times a number:  

Twenty less than eight times the number means that this product is subtracted twenty.  The final answer must be less than eight times the unknown number by twenty.

The correct answer is:  

Example Question #11 : Setting Up Expressions

Select the best choice:  The square of the difference of  and .

Possible Answers:

Correct answer:

Explanation:

Separate the statement by parts.

The difference of  and :  

Square of a the difference of  and :  

The correct answer is:  

Example Question #62 : Basic Single Variable Algebra

Write the expression:  The squared quantity of six less than three times a number squared.

Possible Answers:

Correct answer:

Explanation:

Split up the sentence into parts.

A number squared:  

Three times a number squared:  

Six less than three times a number squared:  

The squared quantity of six less than three times a number squared:  

The answer is:  

Example Question #63 : Basic Single Variable Algebra

Set up the expression:  Seven more than the square root of a number cubed.

Possible Answers:

Correct answer:

Explanation:

Break up the sentence into parts.

A number cubed:  

The square root of a number cubed:  

Seven more than the square root of a number cubed: 

The answer is:  

Example Question #11 : Expressions

Set up the expression:  The square root of six times a number.

Possible Answers:

Correct answer:

Explanation:

Write the expression by splitting up the statement into parts.

Six times a number:  

The square root of six times a number:  

The expression is:  

Example Question #65 : Basic Single Variable Algebra

Set up the expression:  The difference of three times a number and another number cubed.

Possible Answers:

Correct answer:

Explanation:

Let  be a number, and let  be another number.

Set up the parts.

Three times a number:  

Another number cubed:  

The difference of three times a number and another number cubed:

The answer is:  

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