Solve the problem.
70)
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must
be sold to break even.
C(x) =3000x +91,000
R(x) =10,000x
70)
A)
6 units
B)
13 units
C)
14 units
D)
15 units
Solve the system. If there is no solution or if the system’s equations are dependent, so state.
71)
x – y + z = – 1
x + y + z = – 9
x + y – z = – 7
71)
A)
{(–4, –4, –1)}
B)
infinitely many solutions; dependent equations
C)
{(–4, –1, –4)}
D)
no solution or
A
Solve the system by the addition method.
72)
4x – 3y=8
–12x + 9y= – 32
72)
A)
{(x, y)| 4x – 3y =8}
B)
(3, 4)
C)
D)
1
3, –1
4
C
Write the augmented matrix for the system of equations.
73)
x =6
y =7
z =1
73)
A)
[6 7 1 1]
B)
[6 7 1 0]
C)
6 0 0 1
0 7 0 1
0 0 1 1
D)
1 0 0 6
0 1 0 7
0 0 1 1
D
B
Solve the system by the substitution method.
74)
5x +y=14
5x +y=24
74)
A)
{(x, y) 5x + y =14}
B)
{(10, 4)}
C)
{(8, 9)}
D)
Solve the problem.
75)
Given the cost function, C(x), and the revenue function, R(x), find the dollar amount coming in and
going out at the break–even point. Round to the nearest dollar if necessary.
C(x) =1.4x +880
R(x) =2.5x
75)
A)
$800
B)
$564
C)
$344
D)
$2000
D
76)
A chemist needs 50 milliliters of a 38% solution but has only 35% and 40% solutions available. Find
how many milliliters of each that should be mixed to get the desired solution.
76)
A)
30 milliliters of 35%; 30 milliliters of 40%
B)
20 milliliters of 35%; 30 milliliters of 40%
C)
30 milliliters of 35%; 20 milliliters of 40%
D)
30 milliliters of 35%; 40 milliliters of 40%
B
Solve the system by any method.
77)
5x – 4y = – 3
–8y = – 6– 10x
77)
A)
(0, 0)
B)
(5, –4)
C)
{(x, y) 5x – 4y = – 3}
D)
C
D
Solve the problem.
78)
A company’s expenses included many factors. In 2012, travel costs were 2.04% of the expense
budget, increasing by 0.22% of the total expense budget per year. In 2012, office supplies were
5.73% of the expense budget, increasing by 0.02% of the total expense budget per year. Write a
system of equations with two functions. Write one function that models the cost of travel as a
percentage of the total expense budget x years after 2012, and another function that models the cost
of office supplies as a percentage of the total expense budget x years after 2012.
78)
A)
y = – 0.22x +2.04
y = – 0.02x +5.73
B)
y =0.22x
y =0.02x
C)
y =0.22x +2.04
y =0.02x +5.73
D)
y =2.04x +0.22
y =5.73x +0.22
Determine if the given ordered triple is a solution of the system.
79)
(0, 4, –4)
x – y + 2z = – 12
5x + z = – 4
x + 2y + z =4
79)
A)
solution
B)
not a solution
Solve the system by graphing.
80)
x = – y
y + x = 6
80)
A)
{(x, y) y + x = 6}
B)
C)
{(1, 1)}
D)
{(1, 5)}
Solve the system by the substitution method.
81)
5x +3y =80
2x +y=30
81)
A)
{(0, 10)}
B)
{(10, 10)}
C)
D)
{(x, y) 2x + y = 30}
Evaluate the determinant.
82)
–1 3
2 1
82)
A)
5
B)
–7
C)
7
D)
–5
Write a system of linear equations in three variables, and then use matrices to solve the system.
83)
There were approximately 100,000 vehicles sold at a particular dealership last year. The dealer
tracks sales by age group for marketing purposes. The percentage of 36– to 59–year–old buyers
and the percentage of buyers 60 and older combined exceeds the percentage of buyers 35 and
younger by 38%. If the percentage of buyers in the oldest group is doubled, it is 30% less than the
percentage of users in the middle group. Find the percentage of buyers in each of the three age
groups.
83)
A)
13% 35 and younger; 56% 36–59 year olds; 31% 60 and older
B)
31% 35 and younger; 56% 36–59 year olds; 13% 60 and older
C)
33% 35 and younger; 53% 36–59 year olds; 14% 60 and older
D)
25% 35 and younger; 58% 36–59 year olds; 17% 60 and older
Solve the system by any method.
84)
1
2x +1
2y =8
1
5x –1
5y = – 2
5
84)
A)
(6, 10)
B)
(–7, 10)
C)
D)
(7, 9)
Evaluate the determinant.
85)
1
3
1
4
–11
6
5
12
85)
A)
–103
144
B)
43
72
C)
1
54
D)
–23
72
Determine if the given ordered triple is a solution of the system.
86)
(–4, 5, –3)
x – y + z =4
x + y + z = – 2
x + y – z =6
86)
A)
not a solution
B)
solution
Use Cramer’s rule to solve the system.
87)
8x –9y –z= – 44
x+4y +6z =59
4x +y+z=32
87)
A)
{(9, 3, 9)}
B)
{(6, 7, 3)}
C)
{(5, 9, 3)}
D)
{(5, –9, –3)}
Solve the system by the substitution method.
88)
x+7y = – 2
3x +y=34
88)
A)
B)
{(12, –2)}
C)
{(–2, 3)}
D)
{(x, y) x + 7y = – 2}
Solve the problem.
89)
The graph shows the results of an ongoing survey of 500 random students at State University from
2007 through 2012. The survey asked whether students bought the majority of their music on CD or
if they downloaded the majority of their music as MP3 files from the internet. Use the graph to
estimate the point of intersection. In what year was the number of students who bought the
majority of their music on CDs and the number of students who downloaded the majority of their
music as MP3 files the same? How many students were there for each?
89)
A)
(2010, 250); 2010; 250 students
B)
(2010, 200); 2010; 200 students
C)
(2009, 300); 2010; 300 students
D)
(2009, 250); 2009; 250 students
Solve the system by the addition method.
90)
2x +8y = – 24
2x +2y =12
90)
A)
{(–12, 2)}
B)
{(x, y) 2x + 2y =12}
C)
D)
{(12, –6)}
D
A
Solve the problem.
91)
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3
hours to prepare, 2 hours to paint, and 8 hours to fire. A tree takes 15 hours to prepare, 3 hours to
paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If
the workshop has 105 hours for prep time, 78 hours for painting, and 89 hours for firing, How
many of each can be made?
91)
A)
5 wreaths, 3 trees, 6 sleighs
B)
7 wreaths, 6 trees, 4 sleighs
C)
6 wreaths, 5 trees, 3 sleighs
D)
3 wreaths, 6 trees, 5 sleighs
92)
A basketball player scored 26 points in a game. The number of three–point field goals the player
made was 26 less than three times the number of free throws (each worth 1 point). Twice the
number of two–point field goals the player made was 13 more than the number of three–point field
goals made. Find the number of free throws, two–point field goals, and three–point field goals that
the player made in the game.
92)
A)
10 free throws; 7 two–point field goals; 4 three–point field goals
B)
9 free throws; 7 two–point field goals; 1 three–point field goals
C)
9 free throws; 1 two–point field goals; 7 three–point field goals
D)
9 free throws; 8 two–point field goals; 3 three–point field goals
Solve the system by graphing.
93)
3x +y=11
9x +3y =33
93)
A)
{(x, y) 3x + y =11}
B)
{(5, –4)}
C)
{(0, 11)}
D)
Solve the system by the addition method.
94)
9x +16y=16
7x –8y = – 8
94)
A)
{(0, 1)}
B)
C)
{(x, y) 7x –8y = – 8}
D)
{(1, 0)}
Solve the problem.
95)
A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in
safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 11% per
year. How much should they invest in each to realize exactly $14,000 per year?
95)
A)
$90,000 at 5% and $70,000 at 11%
B)
$100,000 at 11% and $60,000 at 5%
C)
$110,000 at 11% and $50,000 at 5%
D)
$100,000 at 5% and $60,000 at 11%
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars.
Use the information in the figure to answer the question.
96)
How many binoculars must be produced and sold for the company to break even?
96)
A)
750 binoculars
B)
2700 binoculars
C)
2250 binoculars
D)
1500 binoculars
Evaluate the determinant.
97)
434
521
346
97)
A)
–11
B)
–7
C)
267
D)
7
Solve the problem.
98)
The three points (x1, y1), (x2, y2), and (x3, y3) are collinear if
x1y11
x2y21
x3y31
= 0. Are the points (–8, –5),
(0, 10), and (–40, –65) collinear?
98)
A)
No
B)
Yes
99)
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must
be sold to break even.
C(x) =11x +19,000
R(x) =30x
99)
A)
1001 units
B)
1000 units
C)
1002 units
D)
388 units
Determine whether the given ordered pair is a solution to the system.
100)
(2, 1)
y =1
x =2y
100)
A)
solution
B)
not a solution
Solve the problem.
101)
Three trains one eastbound, one westbound, and one northbound leave a city at the same time.
The speed of the northbound train is 10 miles per hour greater than the speed of the eastbound
train. After 4 hours, the distance between the westbound train and the eastbound train is 360 miles.
Twice the speed of the westbound train is 50 miles per hour more than the speed of the northbound
train. Find the speeds of the three trains.
101)
A)
eastbound, 50 mph; westbound, 50 mph; northbound, 40 mph
B)
eastbound, 40 mph; westbound, 50 mph; northbound, 50 mph
C)
eastbound, 50 mph; westbound, 50 mph; northbound, 60 mph
D)
eastbound, 30 mph; westbound, 60 mph; northbound, 50 mph
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars.
Use the information in the figure to answer the question.
102)
At the break–even point both cost and revenue are what?
102)
A)
$1500
B)
$2700
C)
$750
D)
$2250
Use Cramer’s rule to solve the linear system.
103)
–2x +3y –z= – 4
x+5y –4z =17
2x +y+z=16
103)
A)
{(6, 3, 1)}
B)
{(6, –3, –1)}
C)
{(7, 1, 1)}
D)
{(3, 1, 3)}
Solve the system. If there is no solution or if the system’s equations are dependent, so state.
104)
–2x –3y +9z = – 7
–9x +5y –6z =2
–4x –6y +18z=2
104)
A)
{(–7, 2, 2)}
B)
infinitely many solutions; dependent equations
C)
{(2, 2, –1)}
D)
no solution or
Solve the system by the substitution method.
105)
y= – 3x +13
2x +9y = – 8
105)
A)
{(5, –2)}
B)
{(x, y) 3x + y = 13}
C)
D)
{(–5, 2)}
Solve the system by the addition method.
106)
3x –5y = – 12
6x +8y = – 24
106)
A)
{(x, y) 3x – 5y = – 12}
B)
{(4, 0)}
C)
D)
{(–4, 0)}
Solve the problem.
107)
Given the cost function, C(x), and the revenue function, R(x), find the dollar amount coming in and
going out at the break–even point. Round to the nearest dollar if necessary.
C(x) =81x +1440
R(x) =99x
107)
A)
$792
B)
$7920
C)
$80
D)
$511
Evaluate the determinant.
108)
4 4 1
–4 0 –1
–4 0 –5
108)
A)
–96
B)
64
C)
96
D)
–64
Solve the system by graphing.
109)
y –5x =2
6y =30x +12
109)
A)
{(1, 1)}
B)
{(–1.5, –1)}
C)
{(x, y) y – 5x =2}
D)
Solve the problem.
110)
Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food
intake to 144 g protein, 122 g fat, and 171 g carbohydrate. According to the health conscious
hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy
meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein,
15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal?
110)
A)
3 mushrooms, 7 meatballs, 6 eggs
B)
6 mushrooms, 3 meatballs, 7 eggs
C)
8 mushrooms, 7 meatballs, 4 eggs
D)
7 mushrooms, 6 meatballs, 3 eggs
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s equations
are dependent, so state.
111)
x+y+z=1
x–y+4z = – 4
2x +2y +2z = – 3
111)
A)
{(1, 4, –4)}
B)
{(1, –4, 4)}
C)
no solution or
D)
infinitely many solutions; dependent equations
Solve the problem.
112)
Ms. Adams received a bonus check for $15,000. She decided to divide the money among three
different investments. With some of the money, she purchased a municipal bond paying 5.5%
simple interest. She invested twice the amount she paid for the municipal bond in a certificate of
deposit paying 4.5% simple interest. Ms. Adams placed the balance of the money in a money
market account paying 3.5% simple interest. If Ms. Adams’ total interest for one year was $585, how
much was placed in each account?
112)
A)
municipal bond: $1250
certificate of deposit: $2500
money market: $11,250
B)
municipal bond: $1500
certificate of deposit: $3000
money market: $10,500
C)
municipal bond: $2000
certificate of deposit: $4000
money market: $9000
D)
municipal bond: $1000
certificate of deposit: $2000
money market: $12,000
Solve the system by any method.
113)
1
4x +1
4y =2
x – y =4
113)
A)
(5, 3)
B)
(–6, 3)
C)
D)
(6, 2)
33
Perform the matrix row operation and write the new matrix.
114)
–6–5 2
1–8 9 R1
R2
114)
A)
–5–13 11
1–8 9
B)
–11 –5 2
–7–8 9
C)
1–8 9
–6–5 2
D)
–5–6 2
–8 1 9
Solve the problem.
115)
Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch. The Annabelle
takes 50% of its catch to Hudson’s, 20% to Captain J’s, and 30% to Mainstreet. The Curly Q takes
40% of its catch to Hudson’s, 40% to Captain J’s, and 20% to Mainstreet. The SloJoe takes 30% of its
catch to Hudson’s, 40% to Captain J’s, and 30% to Mainstreet. One week Hudson’s received 250.1
pounds of shrimp, Captain J’s received 215.6 pounds, and Mainstreet received 163.3 pounds. How
many pounds of shrimp did each boat catch?
115)
A)
Annabelle 195 lb, Curly Q 180 lb, SloJoe 254 lb
B)
Annabelle 195 lb, Curly Q 254 lb, SloJoe 180 lb
C)
Annabelle 180 lb, Curly Q 254 lb, SloJoe 195 lb
D)
Annabelle 254 lb, Curly Q 195 lb, SloJoe 180 lb
Perform the matrix row operation and write the new matrix.
116)
–20 –10 –8–22
113 –3 0
2–7 4 21
1
2R1
116)
A)
–10 –5–4–11
113 –3 0
2–7 4 21
B)
–10 –5–4–22
113 –3 0
2–7 4 21
C)
–10 –5–4–11
1
2
13
2–3
20
1–7
2221
2
D)
–20 –10 –8–22
1
2
13
2–3
20
2–7 4 21
Solve the system by the substitution method.
117)
4x +y=0
–4x +y= – 8
117)
A)
B)
{(x, y) 4x + y = 0}
C)
{(1, –4)}
D)
{(–1, 4)}
Solve the problem.
118)
Given the cost function, C(x), and the revenue function, R(x), write the profit function from
producing and selling x units of the product.
C(x) =59x +3600
R(x) =89x
118)
A)
P(x) = – 30x –3600
B)
P(x) =30x +3600
C)
P(x) =30x –3600
D)
P(x) = – 30x +3600
Determine if the given ordered triple is a solution of the system.
119)
(5, –2, 2)
3x + 2y + z =13
4x – 4y – z =26
4x + y + 5z =28
119)
A)
not a solution
B)
solution
Solve the problem.
120)
One number is 2 less than a second number. Twice the second number is 8 less than 5 times the
first. Find the two numbers.
120)
A)
4 and 6
B)
5 and 7
C)
3 and 5
D)
–6 and –4
Evaluate the determinant.
121)
–7–5
–1 9
121)
A)
–68
B)
68
C)
–58
D)
44
Use Cramer’s rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
122)
6x – 2y=36
12x=34 + 4y
122)
A)
{(–3, –1)}
B)
inconsistent; no solution or
C)
{(5, –3)}
D)
dependent equations; infinitely many solutions
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s equations
are dependent, so state.
123)
x+8y –z= – 1
5x +40y–5z = – 5
4x +2y –4z = – 4
123)
A)
infinitely many solutions; dependent equations
B)
{(1, 8, –1)}
C)
no solution or
D)
{(5, 4, 38)}
Solve the problem.
124)
A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 13 inches longer
than the width. Find the width.
124)
A)
21 in.
B)
8 in.
C)
34 in.
D)
29 in.
Solve the system by the substitution method or the addition method. Identify a system with no solution or infinitely
many solutions, using set notation to express the solution set.
125)
–2x +2y =12
2x +2y =16
125)
A)
{(7, 1)}
B)
{(x, y) –2x + 2y =12}
C)
{(1, 7)}
D)
no solution or
Solve the problem.
126)
Julie and Eric row their boat (at a constant speed) 48 miles downstream for 6 hours, helped by the
current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the
current.
126)
A)
0.5 mph
B)
1 mph
C)
2 mph
D)
7 mph
127)
A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 5 bags
of potato chips, and 4 soft drinks for $22.25. The price of a hot dog is $1.25 more than the price of a
bag of potato chips. The cost of a soft drink is $3.00 less than the price of two hot dogs. Find the cost
of each item.
127)
A)
$2.25 for a hot dog; $1.50 for a bag of potato chips; $1.00 for a soft drink
B)
$1.00 for a hot dog; $2.25 for a bag of potato chips; $1.50 for a soft drink
C)
$2.50 for a hot dog; $1.25 for a bag of potato chips; $1.50 for a soft drink
D)
$2.25 for a hot dog; $1.00 for a bag of potato chips; $1.50 for a soft drink
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s equations
are dependent, so state.
128)
x+5y +4z = – 33
2y +4z = – 16
z= – 2
128)
A)
{(–5, –4, –2)}
B)
infinitely many solutions; dependent equations
C)
no solution or
D)
{(–5, –2, –4)}
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars.
Use the information in the figure to answer the question.
129)
Is there a profit when 581 binoculars are produced?
129)
A)
Yes
B)
No
Use Cramer’s rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
130)
3x +3y =39
3x –3y =15
130)
A)
inconsistent; no solution or
B)
dependent equations; infinitely many solutions
C)
{(9, 4)}
D)
{(4, 9)}
Perform the matrix row operation and write the new matrix.
131)
2–4 1 4
–5 0 4 –2
–1 5 –3–1
–2R1+R2
131)
A)
12 –4–7 8
–5 0 4 –2
–1 5 –3–1
B)
2–4 1 4
–1–8 6 6
–1 5 –3–1
C)
2–4 1 4
–9 8 2 –10
–1 5 –3–1
D)
–9 8 2 –10
–5 0 4 –2
–1 5 –3–1
38
Evaluate the determinant.
132)
300
473
282
132)
A)
–25
B)
114
C)
30
D)
–30
133)
–8 9
4 3
133)
A)
–84
B)
12
C)
–60
D)
60
Write the augmented matrix for the system of equations.
134)
3x + 2y + 9z = – 2
4x + 4z = 4
9x + 5y = 2
134)
A)
3 2 9 2
4 1 4 4
9 5 1 2
B)
3 2 9 –2
4 0 4 4
9 5 0 2
C)
3 2 9 2
4 0 4 4
9 5 0 2
D)
3 2 9 –2
4 1 4 4
9 5 1 2
Solve the system by the addition method.
135)
3x +6y =3
2x +9y = – 8
135)
A)
{(–5, 2)}
B)
C)
{(x, y) 3x + 6y = 3}
D)
{(5, –2)}