57)
A merchant has coffee worth $30 a pound that she wishes to mix with 90 pounds of coffee worth $
80 a pound to get a mixture that can be sold for $40 a pound. How many pounds of the $30 coffee
should be used?
57)
A)
180 lb
B)
225 lb
C)
450 lb
D)
360 lb
58)
A cruise boat travels 84 miles downstream in 4 hours and returns upstream in 12 hours. Find the
rate of the stream.
58)
A)
21 mph
B)
35 mph
C)
14 mph
D)
7 mph
Decide whether or not the ordered pair is a solution of the system.
59)
(–3, 5)
x + y =2
x – y = – 8
59)
A)
Yes
B)
No
Solve the problem.
60)
In a chemistry class, 6 liters of a 4% silver iodide solution must be mixed with a 10% solution to get
a 6% solution. How many liters of the 10% solution are needed?
60)
A)
2.0 L
B)
3.0 L
C)
4.0 L
D)
6.0 L
61)
Midtown Delivery Service delivers packages which cost $1.50 per package to deliver. The fixed cost
to run the delivery truck is $185 per day. If the company charges $6.50 per package, how many
packages must be delivered daily to make a profit of $90?
61)
A)
123 packages
B)
23 packages
C)
55 packages
D)
37 packages
Provide an appropriate response.
62)
Decide if the system has one solution, no solution, or an infinite number of solutions.
6x – y =27
x + 5y =20
62)
A)
One Solution
B)
Infinite number of solutions
C)
No Solution
Solve the problem.
63)
By walking 4 mph for one period of time and 1 mph for another, Roger traveled 12 miles. Had he
walked 1 mph faster throughout, he would have gone 18 miles. How many hours did he walk at
4 mph?
63)
A)
3 hr
B)
1 hr
C)
2 hr
D)
4 hr
Solve by the substitution method.
64)
x – 3y = – 13
7x – 4y = – 23
64)
A)
{(–2, 5)}
B)
{(–1, 4)}
C)
{(1, 5)}
D)
Solve the problem.
65)
Helen Weller invested $13,000 in an account that pays 12% simple interest. How much additional
money must be invested in an account that pays 15% simple interest so that the total interest is
equal to the interest on the two investments at the rate of 13%?
65)
A)
$13,000
B)
$6500
C)
$9000
D)
$10,000
Solve by the substitution method.
66)
0.4x + 0.6y = – 1.4
x – 0.7y = – 5.7
66)
A)
{(–0.5, 0.1)}
B)
{(–5, 1)}
C)
{(1, –5)}
D)
Provide an appropriate response.
67)
If the y term is missing in both of two linear equations, the lines are ________.
67)
A)
the same
B)
parallel or the same
C)
intersecting
D)
parallel
Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
68)
3x + 4y =19
2x + 3y =13
68)
A)
{(1, 5)}
B)
(inconsistent system)
C)
{(3, 7)}
D)
{(5, 1)}
23
Provide an appropriate response.
69)
Decide if the system has one solution, no solution, or an infinite number of solutions.
3x – 9y =6
y =1
3x –2
3
69)
A)
One Solution
B)
Infinite number of solutions
C)
No Solution
Solve the problem.
70)
A company manufactures three products. The graph shows the production from 1986 to 1996. What
was the level of production when the production of C equaled the production of A?
70)
A)
500,000
B)
600,000
C)
800,000
D)
400,000
Solve the system by the elimination method.
71)
7x – 2y =3
–14x + 4y = – 12
71)
A)
{(7, 3)}
B)
{(2, 4)}
C)
D)
7
9, –2
9
Solve the problem.
72)
The sum of two numbers is 42 and their difference is 14. Find the numbers.
72)
A)
30 and 44
B)
14 and 28
C)
12 and 30
D)
29 and 13
Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
73)
4x + y = – 13
x + 4y =8
73)
A)
{(–4, 3)}
B)
{(4, 3)}
C)
{(–3, –1)}
D)
{(–4, –5)}
Indicate whether the statement is true or false.
74)
If one inequality in a system of two linear inequalities contains the “<” symbol and the other
contains the “>” symbol, the graph of the system will have solid boundary lines.
74)
A)
True
B)
False
Solve the problem.
75)
Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time.
Bert walks at 4 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?
75)
A)
4 kilometers per hour
B)
3.5 kilometers per hour
C)
2.5 kilometers per hour
D)
1.5 kilometers per hour
Solve the system by the elimination method.
76)
x + 4y =7
6x + 5y =42
76)
A)
{(–7, –1)}
B)
C)
{(7, 0)}
D)
{(8, 7)}
Solve the problem.
77)
Midtown Delivery Service delivers packages which cost $1.30 per package to deliver. The fixed cost
to run the delivery truck is $119 per day. If the company charges $8.30 per package, how many
packages must be delivered daily to break even?
77)
A)
11 packages
B)
17 packages
C)
12 packages
D)
91 packages
78)
Andy has 20 coins made up of quarters and half dollars, and their total value is $5.75. How many
quarters does he have?
78)
A)
17 quarters
B)
22 quarters
C)
5 quarters
D)
3 quarters
Clear fractions then solve by substitution.
79)
3x
8–3y
5=33
80
4x
7+4y
5=37
35
79)
A)
3
2 , 1
4
B)
3
2 , 3
4
C)
1
4 , 1
2
D)
3
4 , 1
2
Write an expression that illustrates the quantity described.
80)
The monetary value (in dollars) of n nickels
80)
A)
$0.10n
B)
$0.05n
C)
$n
D)
$5n
Without graphing, answer the following questions for the linear system.
(i) Is the system inconsistent, are the equations dependent, or neither?
(ii) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(iii) Does the system have one solution, no solution, or an infinite number of solutions?
81)
x – 4 = y
y + 6 = x
81)
A)
(i) inconsistent
(ii) parallel lines
(iii) no solution
B)
(i) dependent
(ii) one line
(iii) infinite number of solutions
C)
(i) neither
(ii) intersecting lines
(iii) one solution
Write an expression that illustrates the quantity described.
82)
The monetary value (in dollars) of x dimes and y quarters
82)
A)
$0.25x + $0.10y
B)
$0.35(x + y)
C)
$0.10x + $0.25y
D)
$10x + $25y
Graph the solution of the system.
83)
x – 2y
2
x + y 0
83)
27
A)
B)
C)
D)
Clear fractions then solve by substitution.
84)
3x –5y
7= 10
2x
3–9y
7=19
5
84)
A)
3, 7
5
B)
3, 7
9
C)
3, –7
5
D)
3, –7
9
Provide an appropriate response.
85)
Suppose that you start a business manufacturing and selling computers, and it costs you $8526 to
get started. You determine that each computer will cost $1027 to manufacture and you choose to
sell each for $2080. Form a system from two equations, assuming y1=y2, that is, cost = revenue,
and then solve the system. Round to the nearest whole number.
85)
A)
y1=1027x +8526
y2=2080x;
(8, 16,742)
B)
y1=1027x +8526
y2=2080x;
(6, 14,688)
C)
y1=8526x +1027
y2=2080x;
(0, 69,235)
D)
y1=8526x +1027
y2=2080x
(0, 67,181)
Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
86)
3
2x –1
3y = 5
5
2x +2
3y = 12
86)
A)
{(3, 4)}
B)
{(3, 1)}
C)
{(4, 3)}
D)
{(4, –3)}
Without graphing, answer the following questions for the linear system.
(i) Is the system inconsistent, are the equations dependent, or neither?
(ii) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(iii) Does the system have one solution, no solution, or an infinite number of solutions?
87)
x + 2y = 0
y = – 1
2x
87)
A)
(i) inconsistent
(ii) parallel lines
(iii) no solution
B)
(i) neither
(ii) intersecting lines
(iii) one solution
C)
(i) dependent
(ii) one line
(iii) infinite number of solutions
Solve the problem.
88)
Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run
the molding machine is $3806 per week. If the company sells the handles for $3.00 each, how many
handles must be molded weekly to break even?
88)
A)
3806 handles
B)
951 handles
C)
1903 handles
D)
1268 handles
Clear fractions then solve by substitution.
89)
1
2x +1
2y = – 6
x – y =2
89)
A)
{(–6, –6)}
B)
C)
{(5, –6)}
D)
{(–5, –7)}
Graph the solution of the system.
30
90)
3x – 2y 6
x – 1
0
90)
A)
B)
C)
D)
Write an expression that illustrates the quantity described.
91)
The actual speed of a boat that goes 15.3 miles per hour against a current of 2.9 miles per hour
91)
A)
2.9 miles per hour
B)
18.2 miles per hour
C)
15.3 miles per hour
D)
12.4 miles per hour
Graph the solution of the system.
92)
2x + y 4
x – 1 0
92)
A)
B)
C)
D)
32
Solve the problem.
93)
The two largest oil spills together released 302 million gallons of oil into the oceans. The smaller of
the two released 98 million gallons less than the larger of the two. How many million gallons did
the larger one release?
93)
A)
149 million gal
B)
204 million gal
C)
102 million gal
D)
200 million gal
Graph the system of inequalities. Indicate the solution by shading.
94)
2x + 3y 6
x – y 3
y 2
94)
A)
B)
C)
D)
33
Provide an appropriate response.
95)
Suppose that you start a business manufacturing and selling computers, and it costs you $9156 to
get started. You determine that each computer will cost $940 to manufacture. Write and explain a
linear equation which gives your total cost to manufacture x computers in terms of y1 (in dollars).
95)
A)
To find the total cost, multiply the number of computers (x) by the cost per computer (940
dollars) and subtract the fixed cost (9156 dollars). Thus, y1=940x –9156 gives this total cost
(in dollars).
B)
To find the total cost, multiply the number of computers (x) by the cost per computer (9156
dollars) and add the fixed cost (940 dollars). Thus, y1=9156x +940 gives this total cost (in
dollars).
C)
To find the total cost, multiply the number of computers (x) by the cost per computer (9156
dollars) and subtract the fixed cost (940 dollars). Thus, y1=9156x –940 gives this total cost
(in dollars).
D)
To find the total cost, multiply the number of computers (x) by the cost per computer (940
dollars) and add the fixed cost (9156 dollars). Thus, y1=940x +9156 gives this total cost (in
dollars).
96)
Decide if the system has one solution, no solution, or an infinite number of solutions.
x + y =2
x + y =5
96)
A)
One Solution
B)
Infinite number of solutions
C)
No Solution
Solve the problem.
97)
A biologist collected 325 fern and moss samples. There were 29 fewer ferns than moss samples.
How many fern samples did the biologist collect?
97)
A)
177 fern samples
B)
296 fern samples
C)
148 fern samples
D)
103 fern samples
98)
Roberto invested some money at 8%, and then invested $3000 more than twice this amount at 11%.
His total annual income from the two investments was $4830. How much was invested at 11%?
98)
A)
$30,000
B)
$33,000
C)
$9000
D)
$3300
Decide whether or not the ordered pair is a solution of the system.
99)
(1, 2)
3x =5– y
4x =10 – 3y
99)
A)
Yes
B)
No
Without graphing, answer the following questions for the linear system.
(i) Is the system inconsistent, are the equations dependent, or neither?
(ii) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(iii) Does the system have one solution, no solution, or an infinite number of solutions?
100)
x – 2y = 5
2x – 4y = 18
100)
A)
(i) dependent
(ii) one line
(iii) infinite number of solutions
B)
(i) neither
(ii) intersecting lines
(iii) one solution
C)
(i) inconsistent
(ii) parallel lines
(iii) no solution
Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
101)
3x + 2y = 5
–6x – 4y = 5
101)
A)
{(1.5, –1)}
B)
{(–1.5, –1)}
C)
{(1, 1)}
D)
(inconsistent system)
D)
Solve the problem.
102)
Carole‘s car averages 12.8 miles per gallon in city driving and 24.7 miles per gallon in highway
driving. If she drove a total of 598.2 miles on 30 gallons of gas, how much of the gas (to the nearest
gallon) was used for city driving?
102)
A)
14 gallons
B)
23 gallons
C)
12 gallons
D)
18 gallons
D)
103)
The graphs below represent the supply and demand for a product at various prices per unit. How
many units should be produced so that supply equals demand?
103)
A)
42.9 units
B)
2255 units
C)
42,900 units
D)
2250 units
104)
Ron and Kathy are ticket–sellers at their class play, Ron handling student tickets that sell for $2.00
each and Kathy selling adult tickets for $4.50 each. If their total income for 31 tickets was $92.00,
how many did Ron sell?
104)
A)
19 tickets
B)
21 tickets
C)
17 tickets
D)
12 tickets
Clear fractions then solve by substitution.
105)
1
3x +1
3y =1
1
4x –1
4y =7
4
105)
A)
{(–5, –1)}
B)
C)
{(5, –2)}
D)
{(4, –1)}
Solve the problem.
106)
How many liters of a 10% alcohol solution must be mixed with 40 liters of a 50% solution to get a
20% solution?
106)
A)
16 L
B)
12 L
C)
120 L
D)
160 L
Provide an appropriate response.
107)
A student was asked to find ordered pairs that solve the system of equations
x + 2y = 3
–2x – 4y = – 6.
The student claims that (1, 1) and (–1, 2) are the only solutions. Is the student correct?
107)
A)
yes
B)
no
Write an expression that illustrates the quantity described.
108)
The amount of pure antifreeze in a solution of x quarts of 45% antifreeze
108)
A)
0.45x quarts
B)
x quarts
C)
0.45 quarts
D)
45x quarts
A
Clear fractions then solve by substitution.
109)
5x
2–5y
4= – 5
2
8x
9=4
9
109)
A)
1
2 , 3
B)
1
2 , –3
C)
–1
2 , 3
D)
–1
2 , –3
Decide whether or not the ordered pair is a solution of the system.
110)
(–5, –4)
4x + y = – 24
3x + 4y = – 31
110)
A)
No
B)
Yes
Graph the system of inequalities. Indicate the solution by shading.
111)
2x + 3y 6
x – y
3
y 2
111)
A)
B)
38
C)
D)
Graph the solution of the system.
112)
x + 2y 2
x – y 0
112)
A)
B)
39
C)
D)
Decide whether or not the ordered pair is a solution of the system.
113)
(–6, –1)
3x =17 – y
2x =9– 3y
113)
A)
Yes
B)
No
Provide an appropriate response.
114)
When two linear equations are solved for y and the slopes are different and the y–intercepts are
different, the lines are ________.
114)
A)
the same
B)
parallel
C)
intersecting
Indicate whether the statement is true or false.
115)
A system of linear inequalities can have solutions in exactly three of the quadrants.
115)
A)
True
B)
False
Graph the solution of the system.
40