REVIEW - Module 3B: Multi-step equations, Angle Properties, Inequalities,

2

You had $20 to spend on four raffle tickets. After buying them you had $12. How much did each raffle ticket cost?

2

You had $20 to spend on seven advocados. After buying them you had $6. How much did each advocado cost?

3

You had $21 to spend on three pens. After buying them you had $12. How much did each pen cost?

3

You had $25 to spend on seven pencils. After buying them you had $4. How much did each pencil cost?

31

160 students went on a field trip. Five buses were filled and 15 students traveled in cars. How many students were in each bus?

48

166 students went on a field trip. Three buses were filled and 22 students traveled in cars. How many students were in each bus?

54

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

21

The sum of three consecutive odd numbers is 69. What is the smallest of these numbers?

Solution

A number that, when substituted for the variable in both expressions, makes the equation a true number sentence.

8x≤2.40

A store sells 8-foot boards for at most $2.40. What is the cost per foot?

Variable

A symbol (such as a letter) that represents a number (i.e., it is a placeholder for a number).

x - 5≤27

After paying $5.00 for a salad, Taylor has no more than $27.00 left. How much money did she have before buying the salad?

51

Amanda spent $39 on a magazine and some candy bars. If the magazine cost $4 and each candy bar cost $5 then how many candy bars did he buy?

Acute Angle

An angle greater than 0 degrees but less than 90 degrees.

Right Angle

An angle that is 90 degrees.

Obtuse Angle

An angle that is greater than 90 degrees but less than 180 degrees.

Straight Angle

An angle whose measure is exactly 180°.

Angles on a point

Angles around a point will always add up to 360 degrees

Angles on a Line

Angles on one side of a straight line will always add up to 180 degrees.

x/4>13

At a restaurant, Daphaney and her three friends, Amber, Jason and Wilson decided to divide the bill evenly. If each person's part exceeded $13.00, what was the total bill?

6

The sum of three consecutive odd numbers is 93. What is the smallest of these numbers?

40

Briana sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin?

4

Brittney rented a bike from Rob's Bikes. It cost $14 plus $3 per hour. If Sumalee paid $26 then she rented the bike for how many hours?

8

Daniel rented a bike from Jacob's Bikes. It cost $15 plus $7 per hour. If Daniel paid $71 then he rented the bike for how many hours?

16

Daniela spent half of her weekly allowance playing mini-golf. To earn more money her parents let her wash the car for $4. What is her weekly allowance if she ended with $12?

x/2>24.28

Dustin and his best friend Jeremy found some money buried in a field. They split the money evenly, each getting more than $24.28. How much money did they find?

5

Emily's Bikes rents bikes for $16 plus $4 per hour. Leah paid $36 to rent a bike. For how many hours did she rent the bike?

38

For a field trip 20 students rode in cars and the rest filled five buses. How many students were in each bus if 210 students were on the trip?

29

For a field trip 23 students rode in cars and the rest filled nine buses. How many students were in each bus if 482 students were on the trip?

37

For a field trip 25 students rode in cars and the rest filled eight buses. How many students were in each bus if 321 students were on the trip?

40

For a field trip 25 students rode in cars and the rest filled seven buses. How many students were in each bus if 305 students were on the trip?

52

For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

33

For a field trip 8 students rode in cars and the rest filled eight buses. How many students were in each bus if 272 students were on the trip?

18

Hannah had some candy to give to her four cousins. She first took ten pieces for herself and then evenly divided the rest among her cousins. Each child received two pieces. With how many pieces did she start?

8x≥40

How many t-shirts can Banning buy with at least $40 if each t-shirt costs $8.00?

78

How old am I if 400 reduced by 2 times my age is 244?

16

Ian won 40 super bouncy balls playing horseshoes at his school's game night. Later, he gave two to each of his friends. He only has 8 remaining. How many friends does he have?

1.15x≥5.75

If one roll of masking tape costs $1.15, how many rolls can Max buy with at least $5.75?

2

J-Dog had $23 to spend on six notebooks. After buying them he had $11. How much did each notebook cost?

37

Jeremy bought seven boxes. A week later half of all his boxes were destroyed in a fire. There are now only 22 boxes left. With how many did he start?

x + 22.50>32

Last Friday Marissa had $22.50. Over the weekend she received some money for cleaning. She now has over $32.00. How much money did she get for cleaning?

13

Lillian rented a bike from Chad's Bikes. It cost $11 plus $8 per hour. If Lillian paid $51 then she rented the bike for how many hours?

x + 2>7

Lisa is cooking muffins. The recipe calls for more than 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in?

5x≥40

Matt bought 5 of the same packages and the weight of all five packages started at 40 pounds. How much was the weight of one package?

4x<2.52

Max buys a package of 4 batteries for under $2.52. What is the price range for each battery?

4.5x≤18

Max's employer has at most $18.00 to spend on tape measures for his crew. How many can he buy with that amount if each tape measure costs $4.50?

2

Milton had $24 to spend on seven pencils. After buying them he had $10. How much did each pencil cost?

4

Natalie's Bikes rents bikes for $20 plus $3 per hour. Perry paid $32 to rent a bike. For how many hours did he rent the bike?

29

On Tuesday Courtney bought five hats. On Wednesday half of all the hats that she had were destroyed. On Thursday there were only 17 left. How many did she have on Monday?

6

Shaniqua rented a bike from Trevor's Bikes. It cost $14 plus $3 per hour. If Shaniqua paid $32 then she rented the bike for how many hours?

x=20 Vertical angles are congruent.

Solve for x and justify your answer with a vocabulary term.

x=81 degrees, vertical angles y=21 degrees, supplementary angles (78+81+y=180)

Solve for x and y, and justify each answer with a vocabulary term.

x=86 degrees, supplementary angles (25+69+x=180) y=69 degrees, vertical angles

Solve for x and y, and justify each answer with a vocabulary term.

x=23 Linear pairs are supplementary (add up to 180 degrees).

Solve for x.

x=23 degrees The angles shown are supplementary (add up to 180 degrees).

Solve for x.

x=9 Vertical angles are congruent.

Solve for x.

8

The Cooking Club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did the club make?

Vertical Angles

The angles that are opposite each other when two lines cross. They are congruent to each other.

12

The sum of three consecutive even numbers is 42. What is the smallest of these numbers?

15

The sum of three consecutive even numbers is 48. What are the smallest of these numbers?

13

The sum of three consecutive numbers is 42. What is the smallest of these numbers?

23

The sum of three consecutive numbers is 72. What are the smallest of these numbers?

9

The sum of three consecutive odd numbers is 33. What is the smallest of these numbers?

7

The sum of three consecutive odd numbers is 45. What is the smallest of these numbers?

15

The sum of three consecutive odd numbers is 51. What is the smallest of these numbers?

Equivalent Expressions

These are two or more expressions that evaluate to the same number for every substitution of numbers into all the letters in both expressions.

4x>4.32

Trent finds masking tape in packages of 4 rolls for over $4.32. What is the cost of one roll in the package?

Adjacent Angles

Two angles that have a common vertex and a common side.

Supplementary Angles

Two angles that have a sum of 180 degrees.

Complimentary Angles

Two angles that have a sum of 90 degrees

6x<7.26

What is the price of one extension cord if Tevin can buy a package of 6 for under $7.26?

29

You bought a magazine for $3 and six notepads. You spent a total of $27. How much did each notepad cost?

5

You bought a magazine for $3 and two notepads. You spent a total of $13. How much did each notepad cost?

4

You bought a magazine for $4 and some erasers for $3 each. You spent a total of $22. How many erasers did you buy?

5

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

x + 55 ≥ 145

Zach saved $55 toward the purchase of an iPod. The cost of the iPods started at $145. How much more does Zach need to save to buy the iPod?