SAT II Math II : Equations Based on Word Problems

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #1 : Single Variable Algebra

Which of the following phrases can be written as the algebraic expression  ?

Possible Answers:

The absolute value of the difference of a number and eight 

Eight subtracted from the absolute value of a number

The absolute value of the difference of eight and a number

The absolute value of the product of negative eight and a number

Eight decreased by the absolute value of a number

Correct answer:

The absolute value of the difference of eight and a number

Explanation:

 is the absolute value of , which is the difference of eight and a number. Therefore,  is "the absolute value of the difference of eight and a number."

Example Question #1 : Equations Based On Word Problems

Which of the following phrases can be written as the algebraic expression  ?

Possible Answers:

The opposite of the difference of seven and a number

Seven decreased by the opposite of a number

The absolute value of the difference of seven and a number

Seven decreased by the absolute value of a number

The opposite of a number decreased by seven

Correct answer:

Seven decreased by the opposite of a number

Explanation:

 is seven decreased by , which is the opposite of a number; therefore,  is "seven decreased by the opposite of a number."

Example Question #1 : Equations Based On Word Problems

Which of the following phrases can be represented by the algebraic expression  ?

Possible Answers:

One divided into the difference of nine and a number

The multiplicative inverse of the difference of nine and a number

The multiplicative inverse of the difference of a number and nine

Nine less than by the multiplicative inverse of a number 

Nine decreased by the multiplicative inverse of a number 

Correct answer:

The multiplicative inverse of the difference of nine and a number

Explanation:

 is the multiplicative inverse of , which is the difference of nine and a number. Therefore,  is "the multiplicative inverse of the difference of nine and a number".

Example Question #2 : Equations Based On Word Problems

Which of the following phrases can be represented by the algebraic expression 

Possible Answers:

The cube root of the difference of a number and ten

Ten decreased by the cube root of a number

Ten less than the cube root of a number

Ten decreased by three times the square root of a number

Ten less than three times the square root of a number

Correct answer:

Ten less than the cube root of a number

Explanation:

 is ten less than , which is the cube root of a number; therefore,  is "ten less than the cube root of a number".

Example Question #1 : Equations Based On Word Problems

Which of the following phrases can be represented by the algebraic expression 

Possible Answers:

Twenty decreased by the square root of a number

Negative twenty multiplied by the square root of a number

The square root of the difference of a number and twenty

The square root of the difference of twenty and a number 

Twenty less than the square root of a number

Correct answer:

Twenty decreased by the square root of a number

Explanation:

 is twenty decreased by , which is the square root of a number, so  is "twenty decreased by the square root of a number".

Example Question #82 : Equations / Solution Sets

Adult tickets to the zoo sell for ; child tickets sell for . On a given day, the zoo sold  tickets and raised  in admissions. How many adult tickets were sold?

Possible Answers:

Correct answer:

Explanation:

Let  be the number of adult tickets sold. Then the number of child tickets sold is .

The amount of money raised from adult tickets is ; the amount of money raised from child tickets is . The sum of these money amounts is , so the amount of money raised can be defined by the following equation:

To find the number of adult tickets sold, solve for :

 adult tickets were sold.

Example Question #1 : Equations Based On Word Problems

Sarah sells lemonade at the concession stands.  She charges fifty cents per cup of lemonade, and twenty five cents for refills.  What is the equation that represents the total that she will make from the lemonade stand using the variables cups  and refills ?

Possible Answers:

Correct answer:

Explanation:

 Sarah charges fifty cents per cup of lemonade:

Sarah charges twenty five cents for refills:

Set up the equation by adding the totals.

The answer is:  

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