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

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Question

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

Answer

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 , 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.

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Question

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

Answer

$\left |8-a \right |$ 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."

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Question

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

Answer

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

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Question

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

Answer

$\frac{1}{9 - x}$ 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".

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Question

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

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

Answer

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

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Question

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

$20 - \sqrt{x}$

Answer

$20 - \sqrt{x}$ 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".

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Question

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 ?

Answer

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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