a 6g problem bank

Algebra I(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions andzeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world andmathematical situations. The student is expected to: (G) relate direct variation to linear functions and solve problems involvingproportional change.

Problem 1: The cost of a soft drink varies directlywith the number of ounces you buy. If 15 ouncescost $0.60, what would you pay for 32 ounces ofthe soft drink? Show your work.

Problem 2: The number of gallons of gasolineused is directly proportional with the number ofmiles traveled. If traveling 240 miles requires 16gallons, how many gallons would a 600-mile triprequire? Show your work.

Problem 3: If y is directly proportional with x andy = 20 when x = 8, what is the value of y whenx = 24? Show your work.

Ms. Carrie owns a large daycare center. She is required to have 1 supervisor for every 4 trainees. Ifshe currently has 2 supervisors and 20 trainees, what is the minimum number of additional supervisorsshe must hire?

If y is directly proportional with x and y = 36 when x = 30, what is the value of y when x = 25?

The number of soft pretzels processed by a machine in a bakery is directly proportional to the numberof minutes that the machine runs. The machine can process 600 pretzels in 10 minutes of continuousrunning. How many pretzels would the machine process in 45 minutes of continuous running?

A 1,200

B 1,500

C 2,700

D 4,500

A 1,200

B 1,500

C 2,700

D 4,500

A 1,200

B 1,500

C 2,700

D 4,500

The amount of amount of cheese consumed varies directly with the population of the country. It isestimated that on average 700 people in the United States consume 2 tons of cheese yearly. If Texasfollows the same trend as the United States, approximately how many tons of cheese the 20,850,000Texans will consume this year?

F 600 tons

G 16,000 tons

H 60,000 tons

J 100,000 tons

A veterinarian uses a table of values to determine the amount of medicine to give a dog. Hedetermines the table shows a direct variation between the amount of medicine and the weight of thedog. The table prescribes a 12-pound dog be given 40 milligrams of medicine. How much medicineshould the doctor give a 42-pound dog?

A 140 mg

B 180 mg

C 200 mg

D Not Here

When 10 quarts of water was added to an empty aquarium, the weight of the aquarium increased 20.8pounds. The aquarium holds 34 quarts of water when filled to capacity. If the weight of the watervaries directly with the number of quarts used, about how much will the water in the aquarium weighwhen it is filled to capacity?

F 40 pounds

G 50 pounds

H 60 pounds

J 70 pounds

F 600 tons

G 16,000 tons

H 60,000 tons

J 100,000 tons

A 140 mg

B 180 mg

C 200 mg

D Not Here

F 40 pounds

G 50 pounds

H 60 pounds

J 70 pounds

F 600 tons

G 16,000 tons

H 60,000 tons

J 100,000 tons

A 140 mg

B 180 mg

C 200 mg

D Not Here

F 40 pounds

G 50 pounds

H 60 pounds

J 70 pounds

The amount of money Debbie earns varies directly with the number of hours she works. If she earns$540 when she works 40 hours, how much will she earn for working 85 hours?

Record your answer on the grid below. Be sure to use the correct place value.

The amount of money Cheri earns varies directly with the number of hours she works. If she earns$150 when she works 20 hours, how much will she earn for working 50 hours?

F $240

G $275

H $375

J $400

A cake decorator can decorate 6 cakes in 90 minutes. At this rate how many cakes could he decorateduring his 8-hour workday if he takes two 15-minute coffee breaks?

0 0 0 0 0 0 01 1 1 1 1 1 12 2 2 2 2 2 23 3 3 3 3 3 34 4 4 4 4 4 45 5 5 5 5 5 56 6 6 6 6 6 67 7 7 7 7 7 78 8 8 8 8 8 89 9 9 9 9 9 9

+-. . . . . . .

F $240

G $275

H $375

J $400

0 0 0 0 0 0 01 1 1 1 1 1 12 2 2 2 2 2 23 3 3 3 3 3 34 4 4 4 4 4 45 5 5 5 5 5 56 6 6 6 6 6 67 7 7 7 7 7 78 8 8 8 8 8 89 9 9 9 9 9 9

+-. . . . . . .

F $240

G $275

H $375

J $400

0 0 0 0 0 0 01 1 1 1 1 1 12 2 2 2 2 2 23 3 3 3 3 3 34 4 4 4 4 4 45 5 5 5 5 5 56 6 6 6 6 6 67 7 7 7 7 7 78 8 8 8 8 8 89 9 9 9 9 9 9

+-. . . . . . .

Lucy can type 300 words in 5 minutes. How many words can Lucy type in 32 minutes?

F 6,400

G 1,920

H 1,875

J 1,250

Marty is a long distance swimmer. His coach recorded the following data during one of his practicesessions.

If Marty continues to swim at this rate, how many laps will he swim in a 45 minute practice session?

A skater can cover 5 miles in 13 minutes. How many minutes will it take him to cover a distance of 16miles if he travels at the same rate?

G 41.6

H 49.6

J Not Here

Number of Laps Number of Minutes4 58 1014 17.5

F 6,400

G 1,920

H 1,875

J 1,250

G 41.6

H 49.6

J Not Here

F 6,400

G 1,920

H 1,875

J 1,250

G 41.6

H 49.6

J Not Here

The cost of a soft drink varies directly with the number of ounces you buy. If 15 ounces of the softdrink cost $0.60, what will 32 ounces of the soft drink cost?

A $1.28

B $1.30

C $1.44

D $1.92

The cost of a soft drink varies directly with the number of ounces you buy. If 12 ounces cost $0.90,how many ounces of the soft drink could you buy for $7.20?

Two quantities, x and y, are in a relationship where y varies directly with x. The graph of this functioncontains ( 8, 12)� . Which equation describes this relationship?

y x �

A $1.28

B $1.30

C $1.44

D $1.92

y x �

A $1.28

B $1.30

C $1.44

D $1.92

y x �

A $1.28

B $1.30

C $1.44

D $1.92

y x �

Two quantities, x and y, are in a relationship where y varies directly with x. The graph of this functioncontains (4, 5). Which ordered pair would also belong to this function?

A (8, 12)

B (10, 8)

C (16, 20)

D (1, 1.4)

Two quantities, x and y, are in a relationship where y varies directly with x. The graph of this functioncontains (0.5, 6). Which ordered pair would not belong to this function?

F (0.12, 1)

G (1.5, 18)

H (1, 12)

J (2.5, 30)

Which of the following equations do not represent a direct proportional relationship for x and y?

A 6y x

B 4( 2)y x �

C 20yx

Which statement is not true about the graph of a direct proportional function?

F The graph is a line that contains the origin.

G The graph is a line that has a positive x-intercept.

H The graph is a line that whose equation is of the form y mx .

J The graph is a line that whose slope is not zero.

A (8, 12)

B (10, 8)

C (16, 20)

D (1, 1.4)

F (0.12, 1)

G (1.5, 18)

H (1, 12)

J (2.5, 30)

A 6y x

B 4( 2)y x �

C 20yx

A (8, 12)

B (10, 8)

C (16, 20)

D (1, 1.4)

F (0.12, 1)

G (1.5, 18)

H (1, 12)

J (2.5, 30)

A 6y x

B 4( 2)y x �

C 20yx

A (8, 12)

B (10, 8)

C (16, 20)

D (1, 1.4)

F (0.12, 1)

G (1.5, 18)

H (1, 12)

J (2.5, 30)

A 6y x

B 4( 2)y x �

C 20yx