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Algebra III
Linear Functions II
Name_______________
Date________________
1
. A
12
business is installing a wheelchair ramp that rises 22 inches over a
horizontal length of 24 feet.
Is the ramp steeper than
recommended?
1. The maximum recommended slope of a wheelchair ramp is
2. A kitchen appliance manufacturing company determines that the total
cost in dollars of producing x units of a certain blender is
Describe the practical significance of the yC  25x  3500 .
intercept and the slope of this line.
3. The revenue per share for Ebay, Inc. was $0.20 in 1998 and $0.92 in
2001. Assuming linear growth, write an equation that gives the
revenue per share in terms of the year. Predict the revenue per
share for the year 2008.
4. Your publishing company has purchased a $12,000 machine that has a
useful life of 8 years. The salvage value at the end if the 8 years is
$2,000. Write a linear equation that describes the book value of the
machine each year.
5. In 1996, there were 3927 J.C. Penney stores and in 2000 there were
3800 stores. Write a linear equation that gives the number of stores
in terms of the year. Predict the number of stores for the years
2005 and 2010.
6. A microchip manufacturer pays its assembly line workers a daily wage
of $125. In addition, workers receive a piecework rate of $0.75 per
unit produced. Write a linear equation for the daily wage W in terms
of the number of units x produced.
Mr. John Cendrowski
Lower Moreland HS
Algebra III
Linear Functions II
Page 2
7. A roofing contractor purchases a shingle delivery truck with a shingle
elevator for $16,500. The vehicle requires an average expenditure of
$5.25 per hour for fuel and maintenance and the operator is paid
$11.50 per hour.
a) Write a linear equation giving the total cost C of operating this
equipment for t hours.
(Include the purchase cost of the
equipment.)
b) Assuming the customers are charged $67 per hour of machine use,
write an equation for the revenue R derived from h hours of use.
c) Use the profit formula (P = R – C) to write an equation derived
from h hours of use.
d) Use the result of part c to find the break-even point – that is the
number of hours this equipment must be used to yield a profit of 0
dollars.
8. A real estate office handles an apartment complex with 50 units.
When the rent per unit is $580 per month, all 50 units are occupied.
However, when the rent is $625 per month, the average number of
occupied units drops to 47. Assume that the relationship between the
monthly rent p and the demand x is linear.
a) Write the equation of the line giving the demand x in terms of
the rent p.
b) Use this equation to predict the number of units occupied when
the rent is $655.
c) Predict the number of units occupied when the rent is $595.
Mr. John Cendrowski
Lower Moreland HS
Algebra III
Linear Functions II
Page 3
9. The length and width of a rectangular of a rectangular garden are 15
feet and 10 feet respectively. A walkway of width x surrounds the
garden.
a) Write an equation for the perimeter y of the walkway in terms of
x.
b) Determine the slope of the equation from part (a). For each
additional one-foot increase in the width of the walkway,
determine the increase in the perimeter.
10.
A pharmaceutical salesperson receives a monthly salary of $2500 plus
a 7% commission of sales.
a) Write a linear equation for the salesperson’s monthly wage W in
terms of sales S.
b) What would this salesperson’s monthly salary be if he sold
$400,000 worth of pharmaceuticals?
c) How much in monthly sales would have to be made to earn a
monthly salary of $6000?
11. The cost C for making x cases of pet food is given by
C  100x  2600 . Each case of 100 boxes sells for $120.
a) How many cases must be sold for the company to break even?
b) How many cases must be sold for the company to make $5,000?
Mr. John Cendrowski
Lower Moreland HS