Equations Based on Word Problems

SAT Subject Test in Math II · Learn by Concept

Help Questions

SAT Subject Test in Math II › Equations Based on Word Problems

1 - 7

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

$20 - \sqrt{x}$

Twenty decreased by the square root of a number

CORRECT

Twenty less than 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

Negative twenty multiplied by the square root of a number

Explanation

$20 - \sqrt{x}$ is twenty decreased by $\sqrt{x}$ , which is the square root of a number, so $20 - \sqrt{x}$ is "twenty decreased by the square root of a number".

Which of the following phrases can be represented by the algebraic expression $\frac{1}{9 - x}$ ?

The multiplicative inverse of the difference of nine and a number

CORRECT

The multiplicative inverse of the difference of a number and nine

Nine decreased by the multiplicative inverse of a number

Nine less than by the multiplicative inverse of a number

One divided into the difference of nine and a number

Explanation

$\frac{1}{9 - x}$ is the multiplicative inverse of , which is the difference of nine and a number. Therefore, $\frac{1}{9 - x}$ is "the multiplicative inverse of the difference of nine and a number".

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

Seven decreased by the opposite of a number

CORRECT

Seven decreased by the absolute value of a number

The opposite of the difference of seven and a number

The opposite of a number decreased by seven

The absolute value of the difference of seven and a number

Explanation

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

Which of the following phrases can be written as the algebraic expression $\left |8-a \right |$ ?

The absolute value of the difference of eight and a number

CORRECT

The absolute value of the difference of a number and eight

Eight subtracted from the absolute value of a number

Eight decreased by the absolute value of a number

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

Explanation

$\left |8-a \right |$ is the absolute value of , which is the difference of eight and a number. Therefore, $\left |8-a \right |$ is "the absolute value of the difference of eight and a number."

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 ?

CORRECT

$T=\$0.75CR$

Explanation

Sarah charges fifty cents per cup of lemonade:

$\$0.50 C$

Sarah charges twenty five cents for refills:

$\$0.25 R$

Set up the equation by adding the totals.

The answer is:

Adult tickets to the zoo sell for $\$9$ ; child tickets sell for $\$5$ . On a given day, the zoo sold $5\textup,450$ tickets and raised $\$36\textup,330$ in admissions. How many adult tickets were sold?

$2\textup,270$

CORRECT

$2\textup,150$

$2\textup,180$

$2\textup,240$

$2\textup,310$

Explanation

Let be the number of adult tickets sold. Then the number of child tickets sold is $5\textup,450 - A$ .

The amount of money raised from adult tickets is ; the amount of money raised from child tickets is $5 \left (5\textup,450 - A \right )$ . The sum of these money amounts is $\$36,330$ , so the amount of money raised can be defined by the following equation:

$9A + 5 (5\textup,450-A) = 36\textup,330$

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

$9A + 27\textup,250-5A = 36\textup,330$

$4A + 27\textup,250 = 36\textup,330$

$4A + 27\textup,250 - 27\textup,250= 36\textup,330- 27\textup,250$

$4A = 9,080\textup$

$4A \div 4 = 9\textup,080 \div 4$

$A = 2\textup,270$

$2\textup,270$ adult tickets were sold.

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

$\sqrt[3]{x} - 10$

Ten less than the cube root of a number

CORRECT

Ten decreased by the cube root of a number

The cube root of the difference of a number and ten

Ten less than three times the square root of a number

Ten decreased by three times the square root of a number

Explanation

$\sqrt[3]{x} - 10$ is ten less than $\sqrt[3]{x}$ , which is the cube root of a number; therefore, $\sqrt[3]{x} - 10$ is "ten less than the cube root of a number".

Return to subject

AI Study CoachYour personal study buddy

Instant TutoringConnect with a tutor now

Request a TutorGet matched with an expert

Live ClassesJoin interactive classes

Question of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games