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```Name ______________________________________________________ Date _______________________________
Key Math Concepts
Sales tax = price of item × sales tax rate
A piecewise function gives a set of rules for each set of the function. The domain is
defined by the inequalities that follow when.
Guided Exercises
1. Enrique plans to sell his car and places a 6-line ad. His paper charges \$42 for the first
two lines and \$6.75 per extra line to run the ad for one week. What will Enrique’s ad
cost to run for three weeks?
Number of lines over 2: 6 – 2 = ______
Cost of extra lines = number of extra lines × cost of each extra line
Cost of extra lines = 4 × 6.75 = ______
Total cost of ad = number of weeks(cost of the first two lines + cost of extra lines)
Total cost of ad = ______(______ + ______) = ______
The total cost of Enrique’s car ad is ______.
2. The Fort Salonga News charges \$29.50 for a classified ad that is four or fewer lines
long. Each line above four lines costs an additional \$5.25. Express the cost of an ad
algebraically as a piecewise function.
There are two rules:
1) the charges for ads ________________________
2) the charges for ads above ________________________
For rule 1; c(x) = __________
For rule 2; c(x) = __________ + __________(x – 4)
when __________
when __________
The piecewise function is:
 ______
c( x ) = 
 ______ + _____(_______)
64
when ___________
when ____________
Financial Algebra Guided Practice Workbook 5-1
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Name ______________________________________________________ Date _______________________________
Exercises
3. Ms. Boyrer is writing a program to compute ad costs. She needs to enter an algebraic
representation of the costs of a local paper’s ad. The charge is \$32.25 for up to three
lines for a classified ad. Each additional line costs \$6. Express the cost of an ad f(x)
with x lines as a function of x algebraically.
4. Roxanne set up the following split function which represents the cost of an auto
classified ad from her hometown newspaper.
31.50
f (x) = 
31.50 + 5.50( x − 5)
when x ≤ 5
when x > 5
If x is the number of lines in the ad, express the price c(x) of a classified ad from this
paper in words.
5. Dr. Mandel purchased a used car for \$11,325. Her state charges 8% tax for the car,
\$53 for license plates, and \$40 for a state safety and emissions inspection. How much
does she need to pay for these extra charges, not including the price of the car?
{
when x ≤ 6
6. Graph the piecewise function: c(x) = 22.50
22.50 + 5.75(x – 6) when x > 6
What are the coordinates of the cusp? What is the slope of the graph where x > 6?
What is the slope of the graph where x < 6?
7. Express the classified ad rate, \$36 for the first four lines and \$4.25 for each additional
line, as a piecewise function. Use a “Let” statement to identify what x and c(x)
represent.
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Financial Algebra Guided Practice Workbook 5-1
65
Name ______________________________________________________ Date _______________________________
5-2 Buy or Sell a Car
Key Math Concepts
Q1 is the median of the lower half of the data, Q2 is the median, Q3 is the median of the
upper half of the data, and Q4 is the maximum value of the data set.
IQR = Q3 – Q1
To determine outliers, use Upper boundary = Q1 + 1.5(IQR) and
Lower boundary = Q3 – 1.5(IQR)
Guided Exercises
1. Find the mean, median, mode, and range for the data set 34, 56, 44, 200.
Mean = sum of the data ÷ number of items
Mean = (34 + 56 + 44 + 200) ÷ 4 =
= _____
4
Median: write the numbers in ascending order: _____, _____, _____, _____
The number of items is even so frind the average of the middle two numbers.
Median: (44 + 56) ÷ 2 = _____
Range = greatest number – least number = 200 – 34 = _____
The mean is _____, the median is _____, the range is _____, and there is no mode.
2. The data below gives the MPG ratings for cars owned by 15 Placid High School
seniors. How many outliers are in this data set?
15.9, 17.8, 21.6, 25.2, 31.1, 29, 28.6, 32, 34, 14, 19.8, 19.5, 20.1, 27.7, 25.5
In ascending order: ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____,
____, ____, ____, ____
Q2 = the median = ______
Q1 = the median of the lower half = ______
Q3 = the median of the upper half = ______
IQR = Q3 – Q1 = ______ – ______ = ______
Upper boundary = Q1 + 1.5(IQR) = ______ + ______(______) = ______
Lower boundary = Q3 – 1.5(IQR) = ______ – ______(______) = ______
Any number above _____ or below _____ is an outlier. So, there are ___________.
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Financial Algebra Guided Practice Workbook 5-2
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Name ______________________________________________________ Date _______________________________
Exercises
3. A local charity wants to purchase a classic 1956 Thunderbird for use as a prize in a
fundraiser. They find the following eight prices in the paper.
\$48,000
\$57,000
\$31,000
\$58,999
\$61,200
\$59,000
\$97,500
\$42,500
What is the best measure of central tendency to use to get a reasonable estimate for
the cost of the car? Explain.
4. Find the value of x that will make the mean of the following data set equal to 80.
78, 90, 88, 70, x
Given is the list of prices for a set of used original hubcaps for a 1957 Chevrolet. They
vary depending on the condition. Use the data for Exercises 5-12.
\$120 \$50 \$320 \$220 \$310 \$100 \$260 \$300 \$155 \$125
\$600 \$250 \$200 \$200 \$125
5. mean, to the nearest dollar
6. median
7. mode
8. four quartiles
9. range
10. interquartile range
11. boundary for the lower outliers; any lower outliers
12. boundary for the upper outliers; any upper outliers
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Financial Algebra Guided Practice Workbook 5-2
67
Name ______________________________________________________ Date _______________________________
5-3 Graph Frequency Distributions
Key Math Concepts
Q1 is the median of the lower half of the data, Q2 is the median, Q3 is the median of the
upper half of the data, and Q4 is the maximum value of the data set.
IQR = Q3 – Q1
Guided Exercises
7 4 3
1
1 0
2 1
1 1
1. The back-to-back stem-and-leaf plot gives data about the
number of girls (on the left) and boys (on the right) at each high
school in Greene County who purchased their own cars with
money they earned working. How many high schools are in
Greene County? What is the mean number of boys who bought
their own cars? Find the median of the distribution of girls.
1
2
3
4
5
0 1 2
3 4
1 7 9
2
1
3|1! 13 girls
1|2 !12 boys
Count the pieces of data on one side. This is the number of schools.
Number of schools = ______
Mean = sum of the data ÷ number of items
Mean (boys) = (10 + 11 +12 + 23 + 24 + 31 + 37 + 39 + 42 + 51) ÷ 10 = ______
Median: The number of items is even. Find the average of the two middle numbers:
30 + 31
= _____
2
There are ______ schools in Green County. A mean of ______ boys bought cars and a
median of ______ girls bought cars.
Median =
2. The boxplot summarizes information about the numbers of hours worked in
December for 220 seniors at Tomah High School. What is the interquartile range?
What is the median? How many students worked 31 hours or less?
IQR = Q3 – Q1 = ______ – ______ = ______
Q2 is the median, which is the ________ number.
0
10
31
68
80
The interquartile range is ______ and the median is ______.
______ of the data is before the median and ______ is after the median.
______ of the total number of students = ______ × ______ = ______
______ of the students work 31 hours or less.
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Financial Algebra Guided Practice Workbook 5-3
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Name ______________________________________________________ Date _______________________________
Exercises
3. Jerry is looking to purchase a set of used chrome wheels for his SUV. He found 23 ads
for the wheels he wants online and in the classified ads of his local newspaper and
arranged the prices in ascending order, which is given below.
\$350 \$350 \$350 \$420 \$450 \$450 \$500 \$500 \$500 \$500
\$600 \$700 \$725 \$725 \$725 \$725 \$725 \$775 \$775 \$800
\$825 \$825 \$850
Make a frequency table to display the data.
Draw a box-and-whisker plot for the data.
The side-by-side boxplots for distributions A and B were drawn on the same axes.
Use the box plots to answer Exercises 4-8.
4. Which distribution has the greater range?
A
B
5. Which distribution has the smallest interquartile range?
6. What percent of the scores in distribution A is above distribution B’s maximum score?
7. Which distribution has scores that are the most varied?
8. What percent of scores in distribution A are less than distribution B’s first
quartile?
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Financial Algebra Guided Practice Workbook 5-3
69
Name ______________________________________________________ Date _______________________________
5-4 Automobile Insurance
Key Math Concepts
100/200/50 represents 100/200 BI insurance and 50,000 PD insurance.
insurance payment =
+ surcharge
number of payments per year
Guided Exercises
1. Mr. Cousins has 100/300 bodily injury insurance. He was in an auto accident caused
by his negligence. Five people were injured in the accident. They sued in court and
were awarded money. One person was awarded \$150,000, and each of the other two
was awarded \$95,000. How much will the insurance company pay for these lawsuits?
100/300 bodily insurance is \$100,000 per person and \$300,000 per accident.
Of the people with injuries: 1 had \$150,000 in injuries.
\$150,000 > \$100,000, so insurance will pay \$100,000.
2 people had < \$100,000, so insurance will pay \$95,000 each.
Add: ____________ + ____________ + ____________ = ____________
\$290,000 < \$300,000, so the insurance company will pay ____________ of these
lawsuits.
2. The Chow family just bought a second car. The annual premium would have been
a dollars to insure the car, but they are entitled to a 12% discount since another car
is insured by the company. If they pay their premium semiannually, and have to
pay a b dollars surcharge for this arrangement, express their semiannually payment
algebraically.
Discount = decimal × annual premium = 0.12a
Discounted premium = ______ – ______ = ______
insurance payment =
Insurance payment =
a is the same as 1(a).
+ surcharge
number of payments per year
b
The Chow’s discounted annual premium is ________ and their payment is
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Financial Algebra Guided Practice Workbook 5-4
b.
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Name ______________________________________________________ Date _______________________________
Exercises
3. Cai’s annual premium is p dollars. If she pays her premium semiannually, there is a 1%
surcharge on each payment. Write an expression for the amount of her semiannual
payment.
Jake has \$25,000 worth of property damage insurance and \$1,000-deductible collision
insurance. He caused an accident that damaged a \$2,000 sign, and he also did \$2,400
worth of damage to another car. His car had \$2,980 worth of damage done. Answer
Exercises 4-6.
4. How much will the insurance company pay under Jake’s property damage insurance?
5. How much will the insurance company pay under Jake’s collision insurance?
6. How much of the damage must Jake pay for?
7. Allen Siegell has a personal injury protection policy that covers each person in,
on, around, or under his car for medical expenses up to \$50,000. He is involved in
an accident and five people in his car are hurt. One person has \$3,000 of medical
expenses, three people each have \$500 worth of medical expenses, and Allen himself
has medical expenses totaling \$62,000. How much money must the insurance
company pay out for these five people?
Mrs. Lennon has 100/275/50 liability insurance and \$50,000 PIP insurance. During an
ice storm, she hits a fence and bounces into a store front with 11 people inside. Some
are hurt and sue her. A passenger in Mrs. Lennon’s car is also hurt.
8. The store front will cost \$24,000 to replace. There was \$1,450 worth of damage to the
fence. What insurance will cover this, and how much will the company pay?
9. The passenger in the car had medical bills totaling \$20,000. What type of insurance
covers this, and how much will the insurance company pay?
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Financial Algebra Guided Practice Workbook 5-4
71
Name ______________________________________________________ Date _______________________________
5-5 Linear Automobile Depreciaton
Key Math Concepts
Straight line depreciation equation: y = mx + b, where y is the value of the car, x is the
number of years, m is the slope of depreciation, and b is the original price of the car.
Δx
Slope ratio =
Δy
y-intercept: (0, maximum car value); x-intercept: (maximum lifespan, 0)
Guided Exercises
Katie purchased a new car for \$27,599. This make and model straight line depreciates
for 13 years.
1. Identify the coordinates of the x- and y-intercepts for the depreciation equation.
Determine the slope of the depreciation equation.
y-intercept: (0, maximum car value)
x-intercept: (maximum lifespan, 0)
y-intercept: (________, ________)
x-intercept: (________, ________)
Δx
Δy
27.599 − 0
= ________
Slope ratio =
=
0 − 13
Katie’s new car depreciates at a rate of ________ a year.
Slope ratio =
2. Write the straight line depreciation equation that models this situation. Draw the
graph of the straight line depreciation equation.
m = slope = ________
b = y-intercept (original price of car) = ________
y = mx + b
y = ________x + ________
Use the Y= function of the graphing calculator to
create the graph.
72
Financial Algebra Guided Practice Workbook 5-5
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Name ______________________________________________________ Date _______________________________
Exercises
3. The graph of a straight line depreciation equation is shown. Write the straight line
appreciation equation. Use the graph to approximate when the car will be worth half
its original value.
value
\$19,200
\$16,000
\$12,800
\$9,600
\$6,400
\$3,200
0
years
2
4
6
8
10
12
14
4. Caroline purchased a car four years ago at a price of \$28,400. According to research
on this make and model, similar cars have straight line depreciated to zero value after
8 years. How much will this car be worth after 51 months?
5. The straight line depreciation equation for a luxury car is y = –4,150x + 49,800. In
approximately how many years will the car’s value drop by 30%?
6. A new car sells for \$29,250. It straight line depreciates in 13 years. What is the slope
of the straight line depreciation equation?
7. A new car straight line depreciates according to the equation y = –1,875x + 20,625.
What is the original price of the car? How many years will it take for this car to fully
straight line depreciate?
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Financial Algebra Guided Practice Workbook 5-5
73
Name ______________________________________________________ Date _______________________________
5-6
Historical and Exponential
Depreciation
Key Math Concepts
The exponential depreciation formula is y = A(1 – r)x, where A is the car’s standing
value, x is the elapsed time in years, r is the percent of depreciation, and y is the value
of the car after x years.
Guided Exercises
1. Tanya’s new car sold for \$23,856. Her online research indicates that the car will
depreciate exponentially at a rate of 6__38 % per year. Write the exponential depreciation
formula for Tanya’s car.
A is the starting value, or 23,856
r is the percent depreciation or, 6__38 %, or __________.
3
% as a decimal.
8
Write 6
y = A(1 – r)x
y = ________(1 – ________)x
The exponential depreciation formula is y = ________(1 – ________)x .
2. Sharon purchased a used car for \$24,600. The car depreciates exponentially by 8%
per year. How much will the car be worth after 5 years? Round your answer to the
nearest penny.
A = ________
r = ______ or ______
x = ________
Write a depreciation equation.
y = A(1 – r)x
y = ________(1 – ________) ___
Substitute.
y = ____________
Sharon’s car will be worth ____________ after 5 years.
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Financial Algebra Guided Practice Workbook 5-6
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Name ______________________________________________________ Date _______________________________
Exercises
3. Brad purchased a five-year old car for \$14,200. When the car was new, it sold for \$24,000.
Find the depreciation rate to the nearest hundredth of a percent.
4. A car exponentially depreciates at a rate of 8.5% per year. Mia purchased a 4-year-old
car for \$17,500. What was the original price of the car when it was new? Round your
answer to the nearest thousand dollars.
5. The screen to the right is from a graphing calculator after running
an exponential regression analysis of a set of automobile data. X
represents years and y represents car value. Using the numbers on
the screen, write the exponential regression equation.
ExpReg
y=a*b^x
a=43754.00259
b=.8223288103
r 2=.8405850061
r=-.9168342304
6. Nancy and Bob bought a used car for \$22,800. When this car was new, it sold for
\$30,000. If the car depreciates exponentially at a rate of 9.2% per year, approximately
how old is the car? Round your answer to the nearest hundredth of a year.
7. A new car sells for \$31,400. It exponentially depreciates at a rate of 4.95% to \$26,500.
How long did it take for the car to depreciate to this amount? Round your answer to
the nearest tenth of a year.
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Financial Algebra Guided Practice Workbook 5-6
75
Name ______________________________________________________ Date _______________________________
5-7 Driving Data
Key Math Concepts
D = R × T, where D is distance, R is the rate, and T is time in hours.
D = M × G, M is miles per gallon, and G is the number of gallons used.
Guided Exercises
1. Ruth is planning a 1,543-mile trip to a math teachers’ conference in San Diego. She
plans to average 50 miles per hour on the trip. At that speed, for how many hours will
D is the distance, or ____________
R is the miles per hour, or ____________
D=R×T
T=D÷R
Rewrite to solve for T.
T = ____________ ÷ ____________ ≈ ____________
Ruth will travel about ______ hours.
2. Francois’ car gets about 12.5 kilometers per liter. He is planning a 1,600-kilometer
to the nearest liter At an average price of \$1.18 per liter, how much should Francois
expect to spend for gas?
D is the distance, or __________
M is the miles per gallon, or __________
D=M×G
G=D÷M
Rewrite to solve for G.
G = __________ ÷ __________ ≈ __________
The total cost will be __________ × __________ = __________
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Financial Algebra Guided Practice Workbook 5-7
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Name ______________________________________________________ Date _______________________________
Exercises
3. A car travels at an average rate of speed of 60 miles per hour for 7__12 hours. How many
miles does this car travel?
4. A car travels m miles in t hours. Express its average speed algebraically.
5. Abby’s car gets approximately 24 miles per gallon. She is planning a 1,200-mile trip.
About how many gallons of gas should she plan to buy? At an average price of \$4.20
per gallon, how much should she expect to spend for gas?
6. Raquel is driving from New York City to Daytona, Florida, a distance of 1,034 miles.
How much time is saved by doing the trip at an average speed of 60 mph as
compared with 55 mph? Round to the nearest half-hour.
7. Ace Car Rental charges customers \$0.18 per mile driven. You picked up a car and the
odometer read x miles and brought it back with the odometer reading y miles. Write
an algebraic expression for the total cost Ace would charge you for mileage use on a
rented car.
8. Juanita has a hybrid car that averages 44 miles per gallon. Her car has a 12-gallon
tank. How far can she travel on one full tank of gas?
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Financial Algebra Guided Practice Workbook 5-7
77
Name ______________________________________________________ Date _______________________________
5-8 Driving Safety Data
Key Math Concepts
s2
, where s is the speed of the car in miles per hour.
20
Total stopping distance = reaction distance + braking distance
Braking distance =
Guided Exercises
1. How many feet does a car traveling at 57 mph cover in one hour? in one minute?
in one second?
57 × 5,280 = 300,960 feet
One mile = 5,280 feet
300 , 960 ft
1 hr
×
= 5,016 feet
hr
60 min
One hour = 60 minutes
5,016 ft 1 min
×
= 83.6 feet
min
60 s
One minute = 60 seconds
A car traveling 57 mph covers ____________ in one hour, ____________ in one
minute, and ____________ in one second.
2. Jerry is driving 35 miles per hour as he approaches a park. A dog darts out into the
street between two parked cars, and Jerry reacts in about three-quarters of a second.
What is his approximate reaction distance?
35 mph × 5,280 ft = ____________ ft per hour
________________ ÷ 60 min = ________ ft per min
________________ ÷ 60s sec ≈ ________ ft per second
Jerry’s car is traveling about __________ per second.
Write a proportion where x is the distance traveled where the reaction time is 0.75 s.
51
x
1 0.75
51(0.75) = x
__________ = x
Jerry’s reaction distance is about ________.
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Financial Algebra Guided Practice Workbook 5-8
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Name ______________________________________________________ Date _______________________________
Exercises
3. How many feet does a car traveling at a mph cover in one hour? in one minute?
in one second?
4. How many kilometers does a car traveling at 50 kph cover in one hour? How many
meters does a car traveling at 50 kph cover in one hour? in one minute? in one
second?
5. Manuel is driving 60 miles per hour on a state road with a 65 mph speed limit. He
sees a fallen tree up ahead and must come to a quick, complete stop. What is his
approximate reaction distance? What is his approximate braking distance? About
how many feet does the car travel from the time he switches pedals until the car has
completely stopped?
6. Anita is driving on the highway at the legal speed limit of 63 mph. She sees a police
3
time is approximately __
4 of a second. Is she far enough away to safely bring the car to
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Financial Algebra Guided Practice Workbook 5-8
79
Name ______________________________________________________ Date _______________________________
5-9 Accident Investigation Data
Key Math Concepts
S = 30 × D × f × n or 30Dfn , where S is the speed of the car, D is the skid distance,
f is the drag factor, and n is the braking efficiency written as a decimal
S
15fr , where r is the radius of the yaw mark.
C2 M
+ , where r is the radius of the yaw mark, C is the length of the chord, and
8M 2
M is the length of the middle ordinate.
r=
Guided Exercises
1. Mark was traveling at 40 mph on a road with a drag factor of 0.85. His brakes were
working at 80% efficiency. To the nearest tenth of a foot, what would you expect the
average length of the skid marks to be if he applied his brakes in order to come to an
immediate stop?
S=
30Dfn
D = 50 feet; f = 1.1; n = 0.85
S
30(
S
)(
)(
)
Substitute.
≈ ______ mph
The minimum speed of the car is ______ mph.
2. Determine the radius of the yaw mark made when brakes are immediately applied
to avoid a collision based upon a yaw mark chord measuring 59.5 feet and a middle
C2 M
r=
+
8M 2
)2 (
)
+
)
8(
2
r ≈ ________
r=
(
Substitute.
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Financial Algebra Guided Practice Workbook 5-9
or duplicated, or posted to a publicly accessible website, in whole or in part.
Name ______________________________________________________ Date _______________________________
Exercises
3. A car is traveling at 52 mph before it enters into a skid. The drag factor of the road
surface is 0.86, and the braking efficiency is 88%. How long might the average skid
mark be to the nearest tenth of a foot?
4. Arami’s car left three skid marks on the road after she slammed her foot on the
brake pedal to make an emergency stop. The police measured them to be 45 feet,
40 feet, and 44 feet. What skid distance will be used when calculating the skid speed
formula?
5. Andrea was traveling down a road at 45 mph when she was forced to immediately
apply her brakes in order to come to a complete stop. Her car left two skid marks that
averaged 60 feet in length with a difference of 6 feet between them. Her brakes were
operating at 90% efficiency at the time of the incident. What was the possible drag
factor of this road surface? What were the lengths of each skid mark?
6. The measure of the middle ordinate of a yaw mark is 7 feet. The radius of the arc is
determined to be 64 feet. What was the length of the chord used in this situation?