9 Weeks

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. During a sale, customers receive an extra discount if they spend $200 or more. So far, Erin’s purchases total $135. Which inequality can be solved to show how many more dollars d she must spend to receive the extra discount?a.b.

____ 2. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions.a.

0 50 100 150 200 2500–50–100–150–200–250

b.

0 50 100 150 200 2500–50–100–150–200–250

c.

0 50 100 150 200 2500–50–100–150–200–250

d.

0 50 100 150 200 2500–50–100–150–200–250

____ 3. The maximum capacity of a theater is 471 people. So far, 254 people are seated in the theater. Which inequality can be solved to show the number of people p that can still enter the theater?a. c.b. d.

____ 4. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then, graph the inequality.a. ;

0 100 200 300 400 5000–100–200–300–400–500

s

b. ;

0 100 200 300 400 5000–100–200–300–400–500

s

c. ;

0 100 200 300 400 5000–100–200–300–400–500

s

d. ;

0 100 200 300 400 5000–100–200–300–400–500

s

____ 5. Susan wants to find out how long it will take her to bike to a store that is 1 mile away, and then turn around and walk home. Susan’s average cycling rate is 6 times her walking rate. Write and simplify an expression for how long it will take Susan to bike to the store, and then turn around and walk home. If her walking rate is 2 miles per hour, how long will it take Susan to bike to the store, and then turn around and walk home?a.

; It will take Susan of an hour, or 35 minutes, to bike to the store, and then turn around and walk home.

b. ; It will take Susan 2 hours to bike to the store, and then turn around and walk home.c.

; It will take Susan of an hour, or 30 minutes, to bike to the store, and then turn around and walk home.

d.; It will take Susan of an hour, or 5 minutes, to bike to the store, and then turn around

and walk home.

____6. .Lawrence's parents pay him a base allowance of $10 per week and $3.20 per hour for extra chores he completes. Mr. Williams pays Lawrence $7.80 per hour to fix broken washing machines at the laundromat. Which equation models Lawrence's total weekly income?a. c.b. d.

____ 7. The Ybarra family is renting a car for a few days. Meinke Rentals charges $20 per day, plus a fixed cleaning fee of $20. The function represents the cost to rent a car from Meinke Rentals for d days. SmartRent charges $25 per day. The function represents the cost to rent a car from SmartRent for d days. Graph and on the same coordinate plane and describe the transformation that takes to .a.

Number of days

Cos

t ($)

S(d)

M(d)

1 2 3 4 5 6 7

102030405060708090

100110120130140150

A vertical shift down 20 units, followed by a vertical stretch by a factor of 1.25.b.

Number of days

Cos

t ($)

S(d)

M(d)

1 2 3 4 5 6 7

102030405060708090

100110120130140150

A vertical stretch by a factor of 1.25, followed by a vertical shift down 20 units. c.

Number of days

Cos

t ($)

M(d)

S(d)

1 2 3 4 5 6 7

102030405060708090

100110120130140150

A vertical compression by a factor of 0.75, followed by a vertical shift up 20 units. d.

Number of days

Cos

t ($)

M(d)

S(d)

1 2 3 4 5 6 7

102030405060708090

100110120130140150

A vertical shift up 20 units, followed by a vertical compression by a factor of 0.75.

____ 8. A factory makes widgets x and gadgets y. Widgets cost $3 and gadgets cost $5 each to make. The boss wants at least 10 widgets and 20 gadgets per day. Total costs need to be at most $300 per day. What system represents this situation?a. c.

b. d.

_____ 9. Analisa is paid $300 each week plus commission on her total sales s. If she sells less than $200, she receives

5% commission; if she sells $200 or more, she receives 8%. Which function can be used to find her total pay P?a. c.

b. d.

____ 10. Mr. Frankel bought 7 tickets to a puppet show and spent $43. He bought a combination of child tickets for $4 each and adult tickets for $9 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?a.

b.

c.

d.

____ 11. Lena made 32 ounces of a fruit drink mix using pineapple juice and grapefruit juice. The number of ounces of pineapple juice in the fruit drink mix is 5 more than 2 times the number of ounces of grapefruit juice in the fruit drink mix. Which graph shows the number of ounces pineapple juice, x, and the number of ounces of grapefruit juice, y, in the fruit drink mix? What system of equations was used to create the graph?a. c.

b. d.

____12. .A music store is selling posters and CDs. The store profits $3.00 from each poster sold and $5.00 from each CD sold. The store needs to make an average profit of $200 per hour to stay in business. Using x as the number of posters sold and y as the number of CDs sold, write and graph an inequality for the number of each item the store needs to sell to stay in business. If 15 posters are sold, how many CDs must be sold? a. ; At most 31 CDs.

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

c. ; At most 31 CDs.

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

b. ; At least 31CDs. d. ; At least 31 CDs.

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

____ 13. Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have the same volume of water? What is that volume of water?a. 5 minutes; 150 gallons c. 5 minutes; 250 gallonsb. 10 minutes; 150 gallons d. 10 minutes; 250 gallons

____ 14. A store is selling posters and T-shirts. The store profits $3.00 from each poster sold and $5.00 from each T-shirt sold. The store needs to make an average profit of $200 per hour from the sales. Using x as the number of posters sold and y as the number of T-shirts sold, write and graph an inequality for the number of each item the store needs to sell to stay in business. If 15 posters are sold, how many T-shirts must be sold?

a. ; At most 31 T-shirts.

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

c. ; At most 31 T-shirts.

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

b. ; At least 31 T-shirts. d. ; At least 31 T-shirts.

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

8 16 24 32 40 48 56 64 72 80 x

8

16

24

32

40

48

56

64

72

y

____ 15. A local supermarket sells chicken for $2.49/lb and pork for $3.19/lb. Todd buys c pounds of chicken and p pounds of pork. Which of the following inequalities represents that Todd only has $40 to spend?

a.b.c.d.

____ 16. The formula for converting degrees Celsius (C) to degrees Fahrenheit (F) is A chemistry student knows that the temperature in degrees Kelvin (K) is 273.15 degrees greater than in degrees Celsius, so

the formula to convert degrees Kelvin to degrees Fahrenheit is What formula can you use to convert degrees Fahrenheit to degrees Kelvin?a. c.

b. d.

____ 17. When x pounds of force is applied to one end of a lever that is L feet long, the resulting force y on the other end is determined by the distance between the fulcrum (the lever's pivot) and the end of the lever on which the x pounds of force is exerted.

The formula relating the forces is What formula can you use to find the length of the lever?a. c.

b. d.

____ 18. The area A of a trapezoid is given by the formula , where and are the lengths of the two parallel sides. Solve the formula for .a. c.

b. d.

____ 19. Which of the following properties would not be used to justify any of the steps below?

a. Subtraction Property of Equalityb. Multiplication Property of Equalityc. Distributive Propertyd. Zero Product Property

____ 20. Which of the following is a graph of the solutions of OR ?a.

b.

c.

d.

____ 21. Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book and reads 2 pages every night. How long will it take Latisha to be further in the book than Sal?a. 3 nights c. 15 nightsb. 11 nights d. 71 nights

____ 22. Safety goggles function best at room temperature, or 75 F. A pair of special safety goggles can function at temperatures that differ from this value by at most 41.3 F. Write and solve an absolute-value inequality to find the range of acceptable temperatures. Graph the solutions.

a.

0 20 40 60 80 100 120 1400–20–40The range of acceptable temperatures is

.b.

0 20 40 60 80 100 120 1400–20–40The range of acceptable temperatures is

OR .c.

30 40 50 60 70 80 90 100 110 120The range of acceptable temperatures is

.d.

30 40 50 60 70 80 90 100 110 120The range of acceptable temperatures is

OR .

Solve the absolute value equation. Graph the solution.

____ 23.a. x = 1 or x = 4

0 1 2 3 4 50–1–2–3–4–5

c. x = 1 or x = 1

0 1 2 3 4 50–1–2–3–4–5

b. x = 1 or x = 2

0 1 2 3 4 50–1–2–3–4–5

d. x = 2 or x = 1

0 2 40–2–4

Solve the inequality. Graph the solution.

____ 24. A furniture maker uses the specification for the width w in inches of a desk drawer. Write the specification as an absolute value inequality. a. c.b. d.

Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)?

____ 25. Let be the reflection of in the x-axis. What is a function rule for ?

a. c.b. d.

What transformations change the graph of f(x) to the graph of g(x)?

What is the graph of the absolute value equation?

____ 26.a.

O 4 8–4–8 x

4

8

12

16

–4

y c.

O 4 8–4–8 x

4

8

12

16

–4

y

b.

O 4 8–4–8 x

4

8

–4

–8

–12

y d.

O 4 8–4–8 x

4

8

12

16

–4

y

What is the graph of the absolute value function?

____ 27.

a.

O 6 12–6–12 x

6

12

–6

–12

y c.

O 6 12–6–12 x

6

12

–6

–12

y

b.

O 6 12–6–12 x

6

12

–6

–12

y d.

O 6 12–6–12 x

6

12

–6

–12

y

Compare each function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the parent function?

____ 28.a.

( 5

4 , 4) x = 5

4 ;

translated to the left 54 units and up 4 units.

b.(54 , –4); x =

54 ;

translated to the left 54 units and down 4 units.

c.(54 , 4); x =

54 ;

translated to the left 54 units, up 4 units, and reflected in the y-axis.

d.( 5

4 , –4); x = 5

4 ;

translated to the right 54 units and up 4 units.

What is the graph of each absolute value inequality?

____ 29. y |x – 1| + 3a.

O 6 12–6–12 x

6

12

–6

–12

y c.

O 6 12–6–12 x

6

12

–6

–12

y

b.

O 6 12–6–12 x

6

12

–6

–12

y d.

O 6 12–6–12 x

6

12

–6

–12

y

____ 30. |x + 5| y – 2a.

O 6 12–6–12 x

6

12

–6

–12

y c.

O 6 12–6–12 x

6

12

–6

–12

y

b.

O 6 12–6–12 x

6

12

–6

–12

y d.

O 6 12–6–12 x

6

12

–6

–12

y

Multiple ResponseIdentify one or more choices that best complete the statement or answer the question.

____ 31. To print custom-designed T-shirts, Maria must pay a $45 fee plus $15 for each T-shirt. What equations could be used to find the number of T-shirts Maria could print with $390?

a.b.c.d.e.

____ 32. A department store offers a frequent-buyers reward card. Every time a customer earns 100 or more points, the customer receives a gift certificate. Each purchase is worth 12 points, and customers automatically earn 25 points when they sign up. Which inequalities could be used to find the number of purchases a customer needs to make to earn the first gift certificate?

a.b.c.d.e.

____ 33. Sal is having a yard sale. He plans to sell his old DVDs and CDs. Combined, he has 75 DVDs and CDs. He prices them at $1.50 per CD and $4.50 per DVD. Let represent the number of DVDs Sal sells and represent the number of CDs Sal sells. He sells all of his DVDs and CDs and earns $262.50. Which of the following equations should be included in a system that reflects the constraints of this situation?

a.b.c.d.e.

____ 34. An object with mass and an object with mass whose centers of mass are a distance apart experience

an attractive gravitational force given by the formula , where is the universal gravitational constant. Solve this formula for , , , and to determine which equations given below are correct.

a.

b.

c.

d.

e.

f.

g.

h.

Matching35. The surface area of a rectangular prism with a given length , width , and height is

. Match each task with the resulting formula.

a. d.

b. e.

c. f.

____ 1. Solving for the length of a rectangular prism with a given width, height, and surface area

____ 2. Solving for the width of a rectangular prism with a given length, height, and surface area

____ 3. Solving for the height of a rectangular prism with a given length, width, and surface area

Short Answer

36. An essay must be at least 500 words long to be accepted. Define a variable and write an inequality for the acceptable number of words in an essay. Graph the solutions.

37. Justin is on the TV game show You Can Price Like a Pro. He is playing the Grocery Store Game. In this game, Justin is shown six grocery-store items without being shown the prices. He must buy multiples of items until he has a total between $20 and $21 inclusive. If he doesn’t reach $20 with his first item, he continues buying items and adding to his total, until he either wins or goes over $21.

Justin began by buying six bottles of hand lotion. One bottle of lotion costs $2.99. That gives Justin a running total of $17.94. He now considers buying packages of gum.

Part A: Justin guesses that one package of gum costs $0.50. Write a compound inequality to find how many packages he should buy.

Part B: Solve your compound inequality from part a. Write your answer as a compound inequality.

Part C: Justin can only buy whole packages of gum. Assuming each package actually costs $0.50, how many could he buy to win the game?

38. A grocery store offers a coupon for $2 off when a customer buys 6 or more bottles of water. The water costs $1.75 per bottle. Shauna uses the function to find the total dollars it costs to buy bottles of water. When she uses the function to find how many bottles she can buy for $5, she finds , so she concludes she could buy 3 bottles of water for $5. Explain what error Shauna made.

39. Rod has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he have?

40. A jet can travel the 6000 km distance between Washington, D.C. and London in 6 h with the wind. The return trip against the same wind takes 7 h 30 min. Find the rate of the jet in still air and the rate of the wind.

41. Solve the following problem. If extra information is given, identify it.

Sharon earned $460 in simple interest on an investment of $6200. Some of the money earned an interest rate of 5%, and the rest earned 8%. Her average rate of interest was 7.4%. How much did she invest at each rate?

42. Julius is flying home to Los Angeles, California, from Boston, Massachusetts. His distance away from home in miles d can be expressed in terms of t hours by the equation . Graph Julius’s distance away from home in miles d after t hours, choosing appropriate scales.

43. A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.

44. A caterer needs to make at least 20 pounds of a mix of cashews and pecans for a party without spending more than $55 to buy the nuts. The mix should have at least twice as many cashews as pecans by weight. The caterer can buy cashews for $2.15 per pound and pecans for $1.80 per pound. Write and graph a system of inequalities to represent this information. Let x represent the weight of cashews used and let y represent the weight of pecans used.

algebraically, and explain.

45. In a strategy video game, you want to hire 50 soldiers (knights and archers) to attack the enemy base. Knights cost 250 gold coins to hire, and archers cost 150 gold coins to hire. You currently have 8900 gold coins. Write a system of equations to represent the constraints. Explain how each equation constrains the values of the variables. Then give the solution.

46. The business leader of a toy-making company needs to determine the number n of employees that can be hired while maintaining a certain profit . Employee wages are dollars per day, and each employee will make toys on average each day. Each product can be sold for dollars and costs dollars to produce. The daily overhead cost is dollars. Write an equation for profit, explaining how you obtained the equation. Then find an equation expressing the number of employees that can be hired as a function of the other variables.

47. You want to know the number of minutes that you can use on a $20.00 phone card. The card company charges $0.50 for the card and $0.10 for each minute used. The equation , where m is the number of minutes on the card, represents this situation. Solve the equation and write a reason for each step. If necessary, round your answer to the nearest hundredth.

Problem

48. The length of any side of a triangle is less than the sum of the lengths of the other two sides of the triangle. If three side lengths do not satisfy this requirement, then a triangle cannot be formed from them.

2xx – 3

7

a. Given the triangle above, use the restriction on side lengths to write three inequalities. Solve all three inequalities for .

b. What values of will satisfy the inequalities you found in part a? Explain how you know.c. Give an example of one set of possible side lengths for the triangle above.

49. A fruit juice company makes two kinds of juice blends, each in 1-gallon bottles. The regular mix uses

gallon of orange juice and gallon of pineapple juice, while the tropical mix uses gallon of orange juice

and gallon of pineapple juice. The company wants to maximize its profit from selling bottles of the regular juice mix and bottles of the tropical juice mix made using the 225 gallons of orange juice and 150 gallons of pineapple juice it currently has on hand.

a. Give four constraints the company must take into consideration to maximize the profit.

b. Graph and shade the region bounded by the constraints from part a.

r

t

c. If the regular juice blend makes a $2.50 profit per bottle sold and the tropical juice blend makes a $1.75 profit per bottle sold, the profit from selling bottles of the regular blend and bottles of the tropical blend is . The maximum profit is the maximum value found when evaluating the profit function at each vertex on the graph (or the point closest to the vertex with values that make sense in context). What is the maximum profit, and how many bottles of each type of juice blend will be sold to make that profit? Assume all manufactured bottles are sold.

50. Your classmate Juan missed the lesson on graphing linear equations using slope-intercept form. You attended the class and want to help Juan understand the material he missed. Assume Juan knows how to graph

Part A: Write an explanation for Juan that describes the y-intercept of a line and what happens to the graph of as you change the y-intercept. Be specific and consider several cases.

Part B: Write an explanation for Juan that describes the slope m of a line and what happens to the graph of as you change the slope. Be specific and consider several cases.

51. Al's Auto Shop charges $149 for parts and $53 per hour of labor for a repair job. Edna's Engine Repair charges a flat fee of $280 for the same job.Part A: Write a system of equations to represent the situation.Part B: Graph the system of equations.Part C: Which shop is cheaper if the job takes 2 hours? 3 hours?

52. Jim is catering a large party. To make one apple pie, he needs 2 pounds of apples. To make one peach pie, he needs 3 pounds of peaches. There are about 42 pounds of apples in one bushel of apples and 48 pounds of peaches in one bushel of peaches.

Part A: Write an inequality to represent the possible numbers of pies Jim can make from one bushel of apples.Part B: Write an inequality to represent the possible numbers of pies Jim can make from one bushel of peaches.Part C: Jim needs to have at least 240 servings of apple pie and 180 servings of peach pie. If one pie contains 6 servings, how many of each type of pie should he make?

Part D: How many bushels of each type of fruit should Jim buy in order to have enough fruit? Will he have leftover fruit? Explain.

53. A classmate has just solved an equation without checking the answer. Unfortunately, the solution has several mistakes. Without re-doing the entire problem, go through each step and explain how the step was obtained. If the step is incorrect, explain the error and the procedure that should have been followed.

Other

54. Ernesto and his family have just finished dinner at a restaurant in a region where meal tax is 5% of the price of the meal. Ernesto leaves a 17% tip. With tax and tip, the total cost is $58.56. The equation

, where p is the price of the meal without tax or tip, can be used to model this situation. Determine which of the following could be steps in calculating the price of the meal .

a. Yes Nob. Yes Noc. Yes No

d. Yes Noe. Yes No