your company wants to print some flyers for advertising a new product. the printer has two options...
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Your company wants to print some flyers for advertising a new product. The printer has two options to produce the flyers. The traditional printing cost $250 for setup and $0.15 per page printed. To print the flyers digitally they charge $50 for setup and $0.20 per page printed.
a. Write equations for the cost to print n flyers using these two printing options.
2.1-1
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Your company wants to print some flyers for advertising a new product. The printer has two options to produce the flyers. The traditional printing cost $250 for setup and $0.15 per page printed. To print the flyers digitally they charge $50 for setup and $0.20 per page printed.
b. Graph the two equations on the same calculator window.
2.1-1
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Your company wants to print some flyers for advertising a new product. The printer has two options to produce the flyers. The traditional printing cost $250 for setup and $0.15 per page printed. To print the flyers digitally they charge $50 for setup and $0.20 per page printed.
c. Find the number of flyers that will result in the same cost for both printing methods.
2.1-1
4
Solve the following system by graphing the equations by hand
2.1-2
12
41
53
y x
y x
5
The percentage of renewable energy produced by using geothermal and wind is given in the table. Source: US Statistical Abstract 2009.
a. Find a model for the percent of renewable energy
produced by using geothermal energy.
2.1-3
Year Geothermal Wind2003 5.37 1.792004 5.43 2.242005 5.28 2.82007 5.12 4.69
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The percentage of renewable energy produced using geothermal and wind is given in the table. Source: US Statistical Abstract 2009.
b. Find a model for the percent of renewable energy
produced by using wind.
2.1-3
Year Geothermal Wind2003 5.37 1.792004 5.43 2.242005 5.28 2.82007 5.12 4.69
7
The percentage of renewable energy produced using geothermal and wind is given in the table. Source: US Statistical Abstract 2009.
c. Estimate the year in which the percentages of
geothermal and wind energy are the same.
2.1-3
Year Geothermal Wind2003 5.37 1.792004 5.43 2.242005 5.28 2.82007 5.12 4.69
( ) 0.82 1.03W t t
( ) 0.08 5.68G t t
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Use the table on the calculator to numerically find the solution to the system.
2.1-4
4 10
3 15
y x
y x
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For each of the following systems of equations, determine if the system is consistent or inconsistent. If the system is consistent determine if the lines are independent or dependent. Give the solution to the system.
a.
2.1-5
6 4
6 2
y x
y x
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For each of the following systems of equations, determine if the system is consistent or inconsistent. If the system is consistent determine if the lines are independent or dependent. Give the solution to the system.
b.
2.1-5
210
50.2 1
y x
y x
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For each of the following systems of equations, determine if the system is consistent or inconsistent. If the system is consistent determine if the lines are independent or dependent. Give the solution to the system.
c.
2.1-5
16
22 4 24
y x
x y
12
Solve the system using the substitution method.
2.2-1
4 5
22
y x
y x
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Using the models from Section 2.1 for geothermal and wind energy, find the year when the amount of geothermal and wind energy produced will be the same.
Where G(t) is the percentage of renewable energy produced by using geothermal energy t years since 2000 and W(t) is the percentage of renewable energy produced by using wind energy t years since 2000.
2.2-2
( ) 0.08 5.68
( ) 0.82 1.03
G t t
W t t
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Solve the following systems using the substitution method.
a.
2.2-3
3 11
5 16
h c
h c
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Solve the following systems using the substitution method.
b.
2.2-3
2 3 12
5 4 39
w b
w b
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As a new sales employee you are given two salary structures to choose from. The first option has a base salary of $1200 per month and 7% commission on sales made. The second option has a base salary of $800 per month and 9% commission on sales made.a. Find equations to represent the two salary options.
2.2-4
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b. Find what sales amount will result in the same monthly salary for both options.
2.2-4
( ) 1200 0.07
( ) 800 0.09
F s s
S s s
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When Raja retired she received a $760,000 lump sum retirement package. She wants to invest this amount in two accounts. The first account pays 4% simple interest and the second account pays 7% simple interest. Raja wants to earn $47,500 per year in interest to live on.a. Write a system of equations that will help Raja find the amount she should invest in each account.
2.2-5
19
b. How much should Raja invest in each account to earn the $47,500 she wants each year?
2.2-5
760000
0.04 0.07 47500
A B
A B
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Solve the following systems. Label each system as consistent or inconsistent. If the system is consistent, determine if the lines are independent or dependent.a.
2.2-6
2.3 4.7
5 11.5 23.5
d a
d a
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Solve the following systems. Label each system as consistent or inconsistent. If the system is consistent, determine if the lines are independent or dependent.b.
2.2-6
5 10
2 10 20
m p
m p
22
Solve the system using the elimination method.
2.3-1
7 3 6
4 6 42
x y
x y
23
Yomaira need 70 ml of 45% saline solution for a science experiment. She has some 60% saline solution and some 20% saline solution. How much of each of these solutions should Yomaira combine to get the 70 ml of 45% saline solution she needs?
2.3-2
24
Solve the system of equations using the elimination method.
2.3-3
4 9 2
12 6 48
a b
a b
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Solve the following systems of equations using the elimination method.a.
2.3-4
5 7 4
3 9 6
x y
x y
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Solve the following systems of equations using the elimination method. b.
2.3-4
2 6 4
7 21 14
m n
m n
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Solve the following inequalities.
a.
b.
2.4-1
6 10 40b
8 12 3 2g g
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Using the printing flyers classroom example from section 2.1 we get the following
n = the number of flyers printed.T(n) = the cost in dollars to print flyers using the
traditional printing method.D (n)= the cost in dollars to print flyers using digital
printing.
Find for what numbers of flyers the traditional printing method would be cheaper than the digital prints.
2.4-3
( ) 250 0.15 ( ) 50 0.20T n n D n n
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The percentage of United States population with high blood cholesterol is given in the table. Source: CDC 1991-2003 Behavioral Risk Factor Surveillance System.
a. Find equations for models of these data.
2.4-4
Year Percent of Women Percent of Men1991 25.4 24.91995 27.3 27.11999 27.6 28.32003 29.4 33
30
The percentage of United States population with high blood cholesterol is given in the table. Source: CDC 1991-2003 Behavioral Risk Factor Surveillance System.
b. Use the models to approximate when the percent of men with high blood cholesterol is higher than the percent of women.
2.4-4
Year Percent of Women Percent of Men1991 25.4 24.91995 27.3 27.11999 27.6 28.32003 29.4 33
( ) 0.33 25.1 ( ) 0.74 23.4W t t M t t
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Solve the inequality numerically using the calculator table.
2.4-5
4 12 5 4x x
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Solve the inequality graphically.
2.4-6
3 4 13x x
33
Solve the following equations.
a.
b.
2.5-1
7 4x
2 5 6 20x
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Solve the following equations.
c.
2.5-1
4 12 8m
35
Estella is driving from Savannah, Georgia to Washington, D.C. Along the way, she will pass through Richmond, Virginia. Estella’s distance from Richmond can be modeled by the function
where D(t) is Estella’s distance in miles from Richmond after driving for t hours. Find the time when Estella will be 40 miles from Richmond.
2.5-2
( ) 460 60D t t
36
Write the given interval using a compound inequality.
a.
b.
2.5-3
37
Solve the following inequalities. Give the solution as an inequality and graph the solution set on a number line.
a.
b.
2.5-4
4 6x
3 8 10x
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A person with mild high blood pressure will have a systolic pressure (first number) that satisfies the inequality
where S is a person’s systolic pressure in millimeters of mercury (mmHg ).Find the range of systolic pressures that people with mild high blood pressure will have.
2.5-5
150 10S
39
Write the given interval using a compound inequality.
2.5-6
40
Solve the following inequalities. Give the solution as an inequality. Graph the solution set on a number line.
a.
b.
2.5-7
3 5x
2 4 9x
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A person with high or low blood pressure will have a diastolic pressure (second number) that satisfies the inequality
where D is a person’s diastolic pressure in millimeters of mercury (mmHg).Find the diastolic blood pressures that would be considered high or low.
2.5-8
75 15D
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A yard equipment manufacturer produces lawn mowers and roto-tillers in the same plant. Each mower requires 4 hours to produce while rototillers require 7 hours to produce. If the plant operates 70 hours per week, what combinations of mowers and rototillers can they produce in a week?
2.6-1
43
Graph the following inequalities by hand:
a.
2.6-2
12
3y x
44
Graph the following inequalities by hand:
b.
2.6-2
24
3y x
45
Graph the following inequalities by hand:
c.
2.6-2
2 5x y
46
Find the inequality for the given graph.
2.6-3
47
The yard equipment manufacturer we discussed with example 1 had a time constraint that they could not exceed 70 hours of production per week. Each mower requires 4 hours to produce while rototillers require 7 hours to produce. The same plant must stay in production at least 40 hours per week.a. Create a system of inequalities to model this situation.
2.6-4
4 7 70M R
48
The yard equipment manufacturer we discussed with example 1 had a time constraint that they could not exceed 70 hours of production per week. The same plant must stay in production at least 40 hours per week.
b. Graph the solution set for this system.
2.6-4
4 7 70
4 7 40
M R
M R
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The yard equipment manufacturer we discussed with example 1 had a time constraint that they could not exceed 70 hours of production per week. The same plant must stay in production at least 40 hours per week.
c. Can the plant produce 8 mowers and 4 rototillers in a week?
2.6-4
4 7 70
4 7 40
M R
M R
50
Kian has $400,000 from a court settlement to invest. Kian plans to invest the money into two accounts, one paying 3% simple interest and the other paying 4% simple interest. Kian would like to earn at least $14,300 per year to support himself while going back to college. How much should he invest in each account to earn at least $14,300 per year?
2.6-5
51
Graph each system of inequalities by hand.
a.
2.6-6
3 4 12
2 1
x y
y x
52
Graph each system of inequalities by hand.
b.
2.6-6
1.2 2
65
5
y x
y x
53
Graph the system of inequalities using a graphing calculator.
2.6-7
3 4
2 1
y x
y x