Q: A company’s profit $P$ is given by $P = 3x - 2y$, where $x$ is the number of products sold and $y$ is the number of defective products. If $x = 100$ and $y = 10$, what is the profit?

$3 \times 100 - 2 \times 10 = 300 - 20 = 280$

Q: A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. Write an algebraic expression for the total cost $C$ if $m$ miles are driven, and find the cost for $m = 150$.

$C = 25 + 0.2m$, so $C = 25 + 0.2 \times 150 = 25 + 30 = 55$

Question 1

A biologist is studying the population of bacteria in a petri dish. The population doubles every hour. If the initial population is 500 bacteria, what will the population be after 5 hours?

Accepted Answer

$500 	imes 2^5 = 16,000$

Question 2

Simplify the expression: $\dfrac{3x^2y}{6xy^2}$

Accepted Answer

$\dfrac{x}{2y}$

Question 3

A chemical solution contains $\dfrac{2}{5}$ liters of acid and $\dfrac{3}{10}$ liters of base. What is the total volume of the solution?

Accepted Answer

$\dfrac{7}{10}$ liters

Question 4

Which of the following is the degree of the polynomial $4x^3y^2 - 7x^2y + 5$?

Accepted Answer

$5$

Question 5

A patient’s medication dosage is calculated by the formula $D = \dfrac{mg}{kg} 	imes W$, where $W$ is the patient’s weight in kilograms. If the recommended dosage is $2 \ mg/kg$ and the patient weighs $70$ kg, what is the total dosage?

Accepted Answer

$140 \ mg$

Question 6

Simplify the expression: $(-2)^3 + 4 	imes (-2)$

Accepted Answer

$-8 + (-8) = -16$

Question 7

Which of the following sets does the number $-\dfrac{7}{2}$ belong to?

Accepted Answer

Rational numbers, Real numbers

Question 8

A company’s profit $P$ is given by $P = 3x - 2y$, where $x$ is the number of products sold and $y$ is the number of defective products. If $x = 100$ and $y = 10$, what is the profit?

Accepted Answer

$3 	imes 100 - 2 	imes 10 = 300 - 20 = 280$

Question 9

Which of the following is the additive inverse of $-15$?

Accepted Answer

$15$

Question 10

Simplify the expression: $\dfrac{5}{8} - \dfrac{1}{4}$

Accepted Answer

$\dfrac{3}{8}$

Question 11

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. Write an algebraic expression for the total cost $C$ if $m$ miles are driven, and find the cost for $m = 150$.

Accepted Answer

$C = 25 + 0.2m$, so $C = 25 + 0.2 	imes 150 = 25 + 30 = 55$

Question 12

Which of the following is the simplified form of $\dfrac{2x^2y}{4xy^2}$?

Accepted Answer

$\dfrac{x}{2y}$

Question 13

A student scored $85$, $90$, and $95$ on three exams. What is the average score?

Accepted Answer

$\dfrac{85 + 90 + 95}{3} = 90$

Question 14

Which of the following is the product of $(-3x^2y)(4xy^3)$?

Accepted Answer

$-12x^3y^4$

Question 15

A rectangular garden has a length of $2x + 3$ meters and a width of $x - 1$ meters. Write an expression for the area and simplify.

Accepted Answer

$(2x + 3)(x - 1) = 2x^2 + 3x - 2x - 3 = 2x^2 + x - 3$

Question 16

Which of the following is the value of $\left(\dfrac{1}{2}\right)^{-3}$?

Accepted Answer

$8$

Question 17

A train travels at a constant speed of $60$ miles per hour. How far will it travel in $2.5$ hours?

Accepted Answer

$60 	imes 2.5 = 150$ miles

Question 18

Simplify the expression: $3(x - 2) + 4(x + 5)$

Accepted Answer

$7x + 14$

Question 19

Which of the following is the solution to the equation $2x - 5 = 11$?

Accepted Answer

$x = 8$

Foundations and Problem Solving in College Algebra: Key Concepts and Practice

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