APPLICATIONS OF LINEAR EQUATIONS
WORKSHEET
1. Business: The cash flow per share for the Hollister Co.
was $0.18 in 1995 and $4.04 in 2003.
Write a linear equation that gives the cash flow per share in terms of
the year. Then, predict the cash flow
per share for the year 2010.
2. Business: In 1999, there were 4076 J.C. Penney stores
and in 2003, there were 1078 stores.
Write a linear equation that gives the number of stores in terms of the
year. Then, predict the number of J.C.
Penney stores in 2010. Is your answer
reasonable? Explain.
3. Business: Quizno’s purchases a
used pizza oven for $875. After five
years, the oven will have to be replaced.
Write a linear equation giving the value of the equipment during the
five years it will be in use.
4. Business: Payless Shoes is offering a 15% discount on
all items. Write a linear equation
giving the sale price, S, for an item with a list price, L.
5. Business:
Dell Computers, Inc. pays its assembly line workers $11.50 per hour. In addition, workers receive a piecework rate
of $0.75 per unit produced. Write a linear equation for the hourly wage
in terms of the number of units, x, produced per hour.
6. Education:
Penn State University had enrollments of 40,571 students in 2000 and
41,289 students in 2004 at its main campus in University Park,
Pennsylvania. Assuming the enrollment
growth is linear, find a linear model that gives the enrollment in terms of the
year. Predict the enrollment in
2010. What is the slope of the
model? Explain its meaning in the
context of the situation.
7. Education:
The University of Florida had enrollments of 36,531 students in 1990 and
48,673 students in 2003. What was the
average annual change (aka slope) in enrollment from 1990 to 2003? Assuming the enrollment growth is linear,
find a linear model that gives the enrollment in terms of the year.
8. Business:
A pharmaceutical salesperson receives a monthly salary of $2,500 plus a
commission of 8% of sales. Write a
linear equation for the salesperson’s monthly wage in terms of sales.
9. Business:
As a sales representative you travel to see customers using your
personal vehicle. For this travel, you
receive $120 per day for lodging and meals plus $0.55 per mile driven. Write a linear equation giving the daily cost
in terms of the number of miles driven.
10.
Business:
As a student, you receive an interest-free loan of $8,250 from a
relative. You will repay $125 per month
until the loan is paid off. Express the
amount (in dollars) remaining to be paid in terms of time (months)
11.
Business:
Suppose that in 2003, a crane was purchased for $200,000. After 10 years, the crane will have a salvage
value of only $20,000. Use linear
depreciation to write an equation for the value of the crane in terms of time
(years).
12.
Business:
Peripheral Visions Inc. produces studio-quality audiotapes of
live concerts. The company places an ad
in a newsletter. The cost of the ad is
$100. Each audiotape costs $20 to
produce, and the company charges $24 per tape.
a.
Express
the cost, C, as a function of x, the number of tapes produced
b.
Express
the revenue, R, as a function of x, the number of tapes sold.
c. Use the formula for profit (P(x) = R(x) -
C(x)) to write an equation for the profit derived from x number of tapes
d. For what value of x, number of
tapes, does the company “break-even” (profit = $0).
13.
Medicine
(Science): It was estimated
that in 1996, there were 22 million HIV infections worldwide with an annual
infection rate of 3.1 million. Write a
linear equation that models the number of worldwide HIV infections during year
x.
14.
Criminal Justice: The murder rate in the United States
remained roughly constant from 1984 to 1990 at 10 murders per 100,000 people
each year. During the same time period,
the murder rate among state and federal inmates decreased linearly from 30 to 8
per 100,000 inmates. Find the equation
of a line that passes through (1984, 30) and (1990, 8). Determine in what year the number of murders
in US is equal to murder rate in prisons (let y =10)
15.
Public Health: In 1985, approximately 0.51% of the
gonorrhea cases diagnosed in the United States were antibiotic resistant and
approximately 8.2% of the gonorrhea cases diagnosed in 1990 were antibiotic
resistant. Determine an equation for the
percentage of gonorrhea cases that were antibiotic resistant in terms of the
year.
16.
Biology:
In 1988, the number of farm pollution incidents was 4000. This number increased roughly at a rate of
280 per year. Find an equation of a
line that describes the number of pollution incidents during year x.
17.
Entertainment: During the 1990s, the percentage of TV
households viewing cable and satellite TV programs increased while the
percentage viewing network affiliate shows (ABC, CBS, NBC, FOX)
generally decreased. In 1993, 40.9% of
TV households were viewing network affiliate shows during primetime, while in
1995, 37.3% of
TV households were viewing network affiliate shows during primetime. Find the equation of the line that describes
the percentage of TV households viewing network affiliate shows in terms of the
year. Predict the percentage of TV
households viewing network affiliate shows in 2009.