Class 2 Handout - Brookdale Community College



Class 2 Handout

Review Activity for Chapter 3

Section 3.1

1. What is the difference between and equation and an expression?

2. Write an equation with one side containing an algebraic expression and the other

side the number 10.

For problems 3-6, translate each into an algebraic expression:

3. The product of a and p.

4. $15 added to the price.

5. Twice the sum of 7 and x.

6. The quotient of x and the sum of y and z.

7. A 12 inch long sub sandwich is cut into two pieces. Choose a variable to represent the length of one piece. Then write an expression that represents the length of the other piece.

Section 3.2

|Ticket Price |Service Charge |Total Cost |

|20 |2 | |

|25 |2 | |

|p |2 | |

8. A ticket outlet adds a service charge of $2 to the price of every

ticket it sells.

a) Complete the pricing chart:

b) Write a formula for the total cost T if the price of a ticket is p dollars.

9. Find the distance covered by a jet if it travels for 3 hours at 550 mph, using the formula d = rt.

10. Find the Celsius temperature reading if the Fahrenheit reading is [pic], using the formula [pic]

11. Evaluate each expression for the given value of the variable:

a) [pic] for a = 2 c) [pic] for [pic]

b) [pic] for [pic] d) [pic] for [pic]

Section 3.3

12. Write each mathematical expression in simpler form, using fewer mathematical

symbols.

a) [pic] [pic] c) [pic]

b) [pic] d) [pic]

13. Explain what it means to simplify an algebraic expression. Give an example.

14. We expressions and we equations.

15. Simplify each expression:

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

16. Which of the following involve area: carpeting a room, fencing a yard, walking

around lake, painting a wall?

Section 3.4

17. Terms with the same variable and exponent are called terms.

18. What is the difference between a term and a factor? Give examples of each.

19. Simplify each by combining like terms, if possible:

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

20. In the formula p = 2w + 2l:

a) What does p represent?

b) What does 2w mean?

c) What does 2l mean?

21. Simplify each expression:

a) [pic] c) [pic]

b) [pic] d) [pic]

22. A is a letter that represents a number.

A is a number that is fixed and does not change in value.

23. Explain how to check if a number is the solution to an equation.

Section 3.5

24. Explain the error in the following problem:

Solve: [pic]

[pic]

[pic]

25. Solve each equation. Write the complete check of the solution.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

26. A shoe salesman receives a commission for every pair of shoes he sells.

Complete the table:

|Type of Shoe |Number Sold |Commission Per |Total Commission($) |

| | |Pair($) | |

|Dress |10 |3 | |

|Athletic |12 |5 | |

|Child’s |x |2 | |

|Sandal |9[pic]x |4 | |

27. After receiving their tax refund, a husband and wife split the refunded money equally. The husband then gave $50 of his money to charity, leaving him with $70. What was the amount of the tax refund?

a) Define your variable: X =

b) Set up your equation:

c) Solve your equation:

d) Answer: The amount of the tax refund was .

Additional Application Problems

For problems 1 and 2, choose a variable to represent one unknown and define it. Then write an expression that represents the other unknown.

1. In 1960, John F. Kennedy was elected President of the United States with a popular vote of only 118,550 votes more than that of Richard M. Nixon. Express how many votes each candidate received.

2. A rectangle is 6 units longer than it is wide. Express the length and width of this rectangle.

For problems 3-7, use the appropriate formula from the following list:

Sale Price = Original Price – Discount

[pic]

Retail Price = Cost + Markup

[pic]

Profit = Revenue – Costs

[pic]

Distance = [pic]

[pic]

Distance Fallen = [pic]

[pic]

Mean = [pic]

Degrees Celsius = [pic]( Degrees Fahrenheit [pic]32)

[pic]

3. A school carnival brought in revenues of $13,500 and had costs of $5300. What was the profit?

4. Find the distance a ball has fallen, in feet, 2 seconds after being dropped from a tall building.

5. Find the average for a bowler who rolled scores of 254, 225, and 238.

6. A store owner buys a pair of pants for $25 and marks them up $15 for sale. What is the retail price of the pants?

7. At a summer resort, visitors can relax by taking a dip in a swimming pool or a lake. The pool water is kept at a constant temperature of [pic]. The water in the lake is [pic]. Which water is warmer, and by how many degrees Celsius?

Class 2 Handout Answer Key

1. An equation contains an equals sign; an expression does not.

2. [pic] and [pic]are examples

3. [pic]

4. $15 + p p = the price

5. 2(7 + x)

6. [pic] or [pic]

7. x is the length of the first piece.

[pic] is the length of the other piece.

8. a)

|Ticket Price |Service Charge |Total Cost |

|20 |2 |$22 |

|25 |2 |$27 |

|p |2 |p+$2 |

b) T = p + $2

9. 1650 miles

10. [pic]C

11. a) 15 c) [pic]1

b) 4 d) [pic]28

12. a) x c) 5x – 10y – 15

b) x + 15 d) 5x

13. Do all operations possible. For example,

[pic]

14. We simplify expressions and solve equations.

15. a) 16 – 4x d)[pic]

b) 12 + 20s e) [pic]

c) [pic] f) [pic]

16. Area: carpeting a room, painting a wall.

17. Like

18. Terms may be added, factors are multiplied.

19. a) 12r d) 0

b) h – 7 e) [pic]

c) [pic] f) [pic]

20. a) Perimeter

b) Twice the width

c) Twice the length

21. a) 9x + 34 c) [pic]

b) 19e – 21 d)[pic]

22. Variable, Constant

23. Substitute it for the variable in the equation and see if it makes the equation true.

24. [pic]was not distributed to both the 2 and x in the parantheses.

25. a) x = 6 d) z = 0

b) b = 3 e) y = [pic]2

c) g = [pic]5 f) x = [pic]25

26.

|Type of Shoe |Number Sold(Pair)|Commission Per |Total Commission($) |

| | |Pair($) | |

|Dress |10 |3 |$30 |

|Athletic |12 |5 |$60 |

|Child’s |x |2 |$2x |

|Sandal |9[pic]x |4 |$4(9[pic]x) |

27. a) x = Amount of refund.

b) [pic]

c) [pic]240

d) $240

Additional Application Problems

1. x = The number of votes JFK received.

y = The number of votes Nixon received.

x = y + 118,550

2. l = The Length

w = The Width

l = 6 + w

3. $8200

4. 64 ft

5. 239

6. $40

7. The swimming pool is warmer by [pic] C

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