some places are expensive; some places are more affordable · 8/29/2011 · lesson 8.1 assignment...

Chapter 8 Assignments • 139

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Lesson 8.1 Assignment

Name ________________________________________________________ Date _________________________

Some Places are Expensive; Some Places are More Affordable Multiple Representations of Problem Situations

1. Mr. Hong is a rare coin collector. He recently bought a coin valued at $5400. It has been

determined that the coin will increase in value by $30 each month. Mr. Hong plans to

sell the coin within 5 years.

a. Name the quantities that change in this problem situation and the quantities that remain

constant. Determine which quantity depends on the other.

140 • Chapter 8 Assignments

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Lesson 8.1 Assignment page 2

b. Complete the table that represents the different number of months for which Mr. Hong could

own the coin. Label the units of measure in the second row.

Number of Months

Value of Coin at Time of Purchase

Total Value of Coin

0

5

5760

6000

34

6840

55

60

c. Consider the range of values from your table in part (b) and choose an upper bound for the

x- and y-axes that is slightly greater than your greatest value. Choose a lower bound of zero

for both. Add the lower and upper bound values to the table shown for each quantity. Then,

calculate the difference between the upper and lower bounds for each quantity and choose an

interval that divides evenly into this number. Add these intervals to the table.

Variable QuantityLower Bound

Upper Bound

Interval

Months Owned

Value of Coin

7718A_C2_Assign_CH08_139-180.indd 140 6/14/11 9:56 AM


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Name ________________________________________________________ Date _________________________

d. Label the graph below using the bounds and intervals from the table. Then, create a graph of

the coin’s value from the initial purchase to month 60.

e. Should the points on the graph be connected by a line?

Are the data continuous or discrete? Explain your reasoning.

f. Describe the relationship between the two quantities represented in the graph.

g. Approximately how much will the coin be worth if Mr. Hong owns it for 3 years? Use the graph

to answer the question and explain your reasoning.



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h. Approximately when will the coin be worth $6600? Use the graph to answer the question and

explain your reasoning.

i. Write an algebraic equation to represent this situation. Define your variables.

j. After owning the coin for 3 years, Mr. Hong wants to sell the coin. He tells a potential buyer it

is worth $6480. The buyer disagrees and says it is worth $5490. Who is correct? Explain your

reasoning in terms of the equation.



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Name ________________________________________________________ Date _________________________

2. Mr. Hong has coins and old stamps for sale. He decides to advertise the items on an internet site

for collectors. It will cost him $84 initially to advertise and $28 for each day he keeps the items on

sale. If Mr. Hong does not want to spend more than $700 on advertising, what is the maximum

number of days he should advertise? Write an equation and show your work.



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Name ________________________________________________________ Date _________________________

Plastic ContainersUsing Two-Step Equations

1. Geoffrey owns the Super Backyard Shed Company. He makes custom built sheds for residential

homeowners, and he buys the majority of his building materials from two large home stores in the

area. Both stores, Build It and All Things Home, offer reward cards for the purchase of lumber. The

more boards that Geoffrey buys at one time, the more points he will earn. The points can then be

used for future purchases. The table shows the number of reward points that he will earn.

Number of Boards Purchased

Store

Build It All Things Home

1 10 5

2 12.5 8

3 15 11

4 17.5 14

5 20 17

6

7

a. Complete the table to show the number of reward points earned for the purchase of 6 and

7 boards. Use the table and scenario to answer each question.

b. What are the variable quantities in this problem situation? State which quantity depends on

the other.


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c. Create graphs for each store’s reward points in terms of the number of boards purchased.

Identify the bounds and intervals. Be sure to label your graph clearly.

Variable QuantityLower Bound

Upper Bound

Interval

Number of Boards

Reward Points

d. Should you connect the points in your graph? Why or why not?

e. How does the number of reward points change when the number of boards bought at Build It is

increased by 1? Explain your reasoning.


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Name ________________________________________________________ Date _________________________

f. How does the number of reward points change when the number of boards bought at

All Things Home is increased by 1? Explain your reasoning.

g. Determine the number of points that would be earned if Geoffrey buys 12 boards at a time from

each store. Show all your work and use a complete sentence in your answer.

Build It:

All Things Home:

h. In determining the number of reward points for each store, what were the similarities?

What were the differences?


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i. What does the expression b 2 1 represent if you use b to represent the number of boards that

Geoffrey buys at one time?

j. Let p represent the number of reward points. Write an equation that represents the number

of reward points that Geoffrey will earn in terms of the number of boards that he buys from

Build It.

k. Use your equation to calculate the number of reward points Geoffrey will earn from Build It if he

buys 30 boards at a time. Show your work.

l. On his last visit to Build It, Geoffrey earned 100 reward points. How many boards did he buy on

the visit?


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Name ________________________________________________________ Date _________________________

Just Another SaturdaySolving More Complicated Equations

1. Greg is buying a snow blower for the upcoming snow season. The model he is interested in is the

Backsaver 2000. This model has a 6-gallon tank for gas and uses 3 __ 4 gallon of gas every hour it is

running.

a. Write an equation to show the amount of gas in the tank, g, in terms of the number of hours, h,

that the blower has been running.

b. The blower has been running for 2 hours. How much gas will still be in the tank?


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c. There are 1 1 __ 2

gallons of gas remaining in the tank. Write the equation that shows the amount of

gas in the tank.

d. Use your equation to determine how many hours the blower has been running. Write a sentence

to describe how to apply operations and inverse operations to solve the equation. Then solve

the equation and verify your solution.



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2. Greg has decided not to buy a snow blower, and instead looks into other ways to get his driveway

clear. A neighbor has a plow attached to his truck and charges $30 for each time he plows the

driveway. Mel’s Landscaping runs a snow-clearing business and charges $50 for the first time they

plow and $25 for each additional time they plow.

a. Complete the table by writing an expression to represent the neighbor’s price and Mel’s price.

Then evaluate the expressions for the given number of snow removals.

Number of Snow Removals

Neighbor’s Price (dollars)

Mel’s Price (dollars)

h

1

2

3

4

5

6

b. When is the cost of snow removal the same for both services?

c. Write an equation that represents the cost of the two services being equal.


Name ________________________________________________________ Date _________________________


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d. Describe the mathematical operations that should be used to solve this equation. Explain your

reasoning.

e. Solve the equation. Show your work.

f. Describe your solution in terms of the situation.

g. If Greg lives in a location that averages 100 inches of snowfall during the winter months, which

service should Greg use? Explain your reasoning.


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Climbing El CapitanMaking Sense of Negative Solutions

1. Tristan is looking for a new car. He has particular interest in an expensive sports car with a list price

of $32,500. Tristan knows that the minute he drives the car off of the lot, it will start to lose value,

or depreciate. He finds out that the car will depreciate to a scrap value of $1000 in 15 years.

a. What is the total change in value of the car in 15 years?

b. What is the average amount of depreciation per year?

c. When the car is exactly 7.5 years old, Tristan decides to sell it to his friend Jovann. What is the

value of the car when Jovann buys it?

d. Assuming the car will depreciate at the same average rate it did when Tristan owned it, what

will be the value of the car after Jovann has owned it for 6 months?


Name ________________________________________________________ Date _________________________


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e. Assuming the car will depreciate at the same average rate it did when Tristan owned it, what

will be the value of the car after Jovann has owned it for two and one-half years?

f. What are the two quantities that are changing in parts (d) and (e)? Which quantity depends on

the other? Define and identify the independent and dependent variables for the quantities you

defined with their units of measure.


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Name ________________________________________________________ Date _________________________

g. Complete the table for the given values. The remaining rows will be filled in later. Then write an

equation or rule to calculate the value of the car given the number of years Jovann has owned

the car.

Number of YearsJovann Owns the Car

Value of the Car

t v

0

0.5

2.5


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h. Use the equation in part (g) to determine how long Jovann has owned the car when it

depreciates to its scrap value of $1000. Enter your results in the table.

i. Use the equation in part (g) to determine how long Jovann has owned the car when it is worth

$22,000. Make sure to show your work. Enter your results in the table in part (f).


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Name ________________________________________________________ Date _________________________

j. Use the equation in part (g) to determine the value of the car 4 years before Jovann purchased

it. Enter your results in the table.

k. Use the equation in part (g) to determine the value of the car 6 1 __ 2 years before Jovann purchased

it. Enter your results in the table.


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l. Use the equation in part (g) to determine when the car was worth its initial value of $32,500.

Enter your results in the table.

m. On the grid, plot the points from the table. Label your axes with the units of measure and draw

the graph of your equation.

v

–2

5000

10000

15000

20000

25000

30000

35000

40000

45000

2 4 6 8–4–6–8 t


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Name ________________________________________________________ Date _________________________

n. Locate the point at t 5 25. What is the value of the car at this point?

o. Write the point in part (n) as an ordered pair. What does the ordered pair mean in the context of

the problem?


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Name ________________________________________________________ Date _________________________

Flying in the OceanRate of Change

1. The Transverse Tire Company produces all types of tires at its factory. Due to fixed costs

associated with running the factory, the company starts with a loss of $200,000, or a profit of

2$200,000, at the beginning of each month. The first major hurdle the company faces each month

is to break even, or reach the point at which the profit is zero. The tires are sold in batches of 1000.

The company earns $40,000 for each batch of tires they manufacture and sell.

a. Identify the two quantities that are changing in this situation, identify the independent and

dependent quantities, and define the variables for these quantities. Then write an equation to

represent the profit the company will make when they manufacture and sell batches of tires.


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b. Use your equation in part (a) to complete the table for this problem situation.

Independent Quantity

Dependent Quantity

Quantities

Units of Measure

Variables

0

1

2

3

4

5

c. What is the unit rate of change in this problem?

d. How much profit would the company make if they manufactured and sold 3 and one-half

batches (or 3500 tires)?


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Name ________________________________________________________ Date _________________________

e. How much profit would the company make if they manufactured and sold 500 tires?

f. How much profit would the company make if they manufactured and sold two and

three-quarters batches (or 2750 tires)?


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g. How many batches of tires does the company have to manufacture and sell to have a profit of

2$190,000?


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Name ________________________________________________________ Date _________________________

h. How many batches of tires does the company have to manufacture and sell to have a

profit of 2$50,000?


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i. How many batches of tires does the company have to manufacture and sell to have a profit of

2$76,000?


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Name ________________________________________________________ Date _________________________

j. Use all of the points generated in parts (d) through (i), and the table values from part (b),

to construct a graph. Plot all the points and then draw the graph to represent the problem

situation.

bp

–200000

–175000

–150000

–125000

–100000

–75000

–50000

–25000

1 2 3 4 5 6 7 8

k. The following year, the company is faced with rising costs of materials, labor, and taxes. The

equation that represents their profit is p 5 2300,000 1 35,000b. What is the unit rate of change

for this equation? What does it represent in the problem situation?


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Name ________________________________________________________ Date _________________________

Emptying a TankUsing Multiple Representations to Solve Problems

The Department of Transportation in each state is responsible for the improvements and repairs of that

state’s roads. One important job is to repaint the road lines that have worn away or faded. A painting

crew is painting a 24-mile stretch of road. They have already completed a total of 9.5 miles of the road.

1. The crew has been painting at a rate of 0.25 mile per hour and continues to paint at the same rate.

a. Identify the two quantities that are changing in this situation, identify the independent and

dependent quantities, and define the variables for these quantities. Then write an equation that

relates the two quantities.

b. What is the unit rate of change in this situation? Explain.

c. How many total miles of the road will be completed if the crew works for another 2 hours?


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d. How many total miles of the road will be completed if the crew works for another 5 hours?

e. How many total miles of the road will be completed if the crew works for another 6 1 __ 2

hours?

f. How many more hours does the crew need to work to complete half of the job?


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Name ________________________________________________________ Date _________________________

g. How many more hours does the crew need to work to complete the job?


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h. After painting the first 9.5 miles of the road, the crew members have a discussion. They all

agree that the 8th mile of the road was the most difficult to paint. One of the crew members

asks how long it had been since they finished the 8th mile. How long ago was it, in hours

worked?


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Name ________________________________________________________ Date _________________________

i. During the crew members’ discussion in part (h), another crew member asks how long it had

been since they began the project. How long ago, in hours worked, did they begin the project

after completing the initial 9.5 miles?


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j. Complete the table.


Dependent Quantity

Quantities

Units of Measure

Variables

0

2

5

6.5

12

24

8

0


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Name ________________________________________________________ Date _________________________

k. Use the table in part (j) to plot the points and graph the equation for this situation. Be sure

to label the axes.

t

y

–30 –20 –10 10

5

10

15

20

25

30

35

40

20 30 40 50

2. A road work crew has 200 gallons of paint left after painting the first 9.5 miles of a 24-mile stretch

of road. The equation that is used to determine the amount of paint they have left is

g 5 200 2 16m, where g represents the gallons of paint remaining and m represents the

number of additional miles painted.

a. How many gallons of paint are left after the crew has painted an additional 5 miles of road?


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b. How many gallons of paint are left after the crew has painted an additional 7.5 miles of road?

c. How many additional miles of the road has the crew painted if they have 20 gallons of

paint left?


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Name ________________________________________________________ Date _________________________

d. How many additional miles of the road has the crew painted if they have 8 gallons of paint left?

e. What is the unit rate of change? Explain.


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f. How many additional miles of the road will the crew have painted when they run out of paint?

Do they have enough paint to do the entire job?


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Name ________________________________________________________ Date _________________________

g. Complete the table.


Dependent Quantity

Quantities

Units of Measure

Variables

0

5

7.5

20

8

0

h. Use the table in part (g) to plot the points and graph the equation for this situation. Be sure to

label the axes.

m

g

4 6 82

25

50

75

100

125

150

175

200

10 12 14 16

some places are expensive; some places are more affordable · 8/29/2011 · lesson 8.1 assignment...

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