Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Solve the problem.
1)
1)
An electronics company kept comparative statistics on two products, A and B. For the years 2003
to 2011, the total number of Product A ever sold (in thousands) is given by the equation
y =77x +200, where x is the number of years since 2003. For that same period, the total number
of Product B ever sold (in thousands) is given by the equation y = – 30x + 434, where x is the
number of years since 2003. Use the substitution method to solve the system and choose the
statement that most accurately describes the solution.
A)
When 369,000 of Product A had been sold, 2.2 times as many of Product B had been sold.
B)
At some point between 2003 and 2011, the company had sold 2200 of each product.
C)
The company sold about 2.2 times as many of Product B as Product A.
D)
At about 2.2 years (to the nearest tenth) since 2003, the company sold the same number of
Product A as Product B.
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
2)
3x + y = – 7
2x + y = – 6
2)
A)
{(1, 4)}
B)
{(–1, –4)}
C)
{(–4, –1)}
D)
no solution;
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
3)
y =1.4x – 3.7
y =0.8x – 3.04
3)
A)
{(1.1, –2.16)}
B)
no solution;
C)
infinitely many solutions; {(x, y) y =1.4x – 3.7} or {(x, y) y =0.8x – 3.04}
D)
{(–1.1, –2.16)}
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
4)
2x – 5y =5
3x – 4y =5
4)
A)
–5
7, 5
7
B)
no solution;
C)
5
7, –5
7
D)
infinitely many solutions; {(x, y) 2x – 5y =5} or {(x, y) 3x – 4y =5}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
5)
x – 2y =16
–2x – 3y =3
5)
A)
no solution;
B)
{(–6, –4)}
C)
{(5, –4)}
D)
{(6, –5)}
Solve the system by the best method. Use set notation to express the solution set.
6)
3x = – 9
x + 5y =17
6)
A)
{(3, –4)}
B)
{(3, 4)}
C)
{(–3, 4)}
D)
no solution;
Solve the problem.
7)
7)
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 238.7 pounds of shrimp, Captain J’s received 212.2 pounds, and Mainstreet received
156.1 pounds. How many pounds of shrimp did each boat catch?
A)
Annabelle 194 lb, Curly Q 260 lb, SloJoe 153 lb
B)
Annabelle 194 lb, Curly Q 153 lb, SloJoe 260 lb
C)
Annabelle 260 lb, Curly Q 194 lb, SloJoe 153 lb
D)
Annabelle 153 lb, Curly Q 260 lb, SloJoe 194 lb
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
8)
x + 2y =2
9x + 3y =3
8)
A)
{(1, 0)}
B)
no solution;
C)
{(–1, 0)}
D)
{(0, 1)}
Solve the problem.
9)
9)
A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter
Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A platter
takes 15 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to
prepare, 15 hours to paint, and 7 hours to fire. If the workshop has 96 hours for prep time, 73
hours for painting, and 101 hours for firing, how many of each can be made?
A)
8 serving bowls, 4 platters, 3 bread baskets
B)
4 serving bowls, 3 platters, 8 bread baskets
C)
9 serving bowls, 5 platters, 4 bread baskets
D)
3 serving bowls, 8 platters, 4 bread baskets
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
10)
x – 3y =3
–3x – 4y = – 22
10)
A)
{(5, 2)}
B)
{(6, 1)}
C)
no solution;
D)
{(–6, 2)}
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
11)
x +3
4y = – 8
x = – 5
11)
A)
{(–5, –4)}
B)
no solution;
C)
{(5, –4)}
D)
{(–5, 4)}
Determine if the given ordered triple is a solution of the system.
12)
12)
(–3, 2, –2)
x + 5y + 3z =1
2y + 4z = – 4
z = – 2
A)
not a solution
B)
solution
5
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
13)
x =8
x = – 5
13)
A)
{(–5, 8)}
B)
{(8, –5)}
C)
no solution;
D)
infinitely many solutions; {(x, y) x =8} or {(x, y) x = – 5}
Solve the problem.
14)
14)
A basketball player scored 31 points in a game. The number of three–point field goals the player
made was 19 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 3 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.
A)
8 free throws; 5 two–point field goals; 7 three–point field goals
B)
9 free throws; 4 two–point field goals; 8 three–point field goals
C)
8 free throws; 4 two–point field goals; 5 three–point field goals
D)
8 free throws; 5 two–point field goals; 4 three–point field goals
15)
15)
A loan officer at a bank has $88,000 to lend and is required to obtain an average return of 8% per
year. If he can lend at the rate of 9% or the rate of 7%, how much can he lend at the 7% rate and
still meet his required return?
A)
$9777.78
B)
$44,000.00
C)
$5500.00
D)
$748,000.00
16)
16)
Julie and Eric row their boat (at a constant speed) 35 miles downstream for 5 hours, helped by the
current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of
the current.
A)
2 mph
B)
6 mph
C)
0.5 mph
D)
1 mph
17)
17)
The radiator in a certain make of car needs to contain 40 liters of 40% antifreeze. The radiator
now contains 40 liters of 20% antifreeze. How many liters of this solution must be drained and
replaced with 100% antifreeze to get the desired strength?
A)
13.3 liters
B)
10.0 liters
C)
16 liters
D)
20 liters
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
18)
y = x + 3
y =3x + 7
18)
A)
{(2, –1)}
B)
{(1, –2)}
C)
{(–2, 1)}
D)
no solution;
Determine whether the system is inconsistent, dependent, or neither.
19)
3x + y = – 6
–2y + 2z = – 2
3x + 5y – 4z = – 2
19)
A)
neither
B)
dependent
C)
inconsistent
Solve the problem.
20)
20)
One number is 2 less than a second number. Twice the second number is 40 more than 5 times
the first. Find the two numbers.
A)
–13 and –11
B)
–11 and –9
C)
10 and 12
D)
–12 and –10
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
21)
x = – y
y + x = 6
21)
A)
no solution;
B)
infinitely many solutions; {(x, y) y + x = 6} or {(x, y) x = – y}
C)
{(1, 5)}
D)
{(1, 1)}
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
22)
5x + y = – 16
2x + 3y =4
22)
A)
{(4, 4)}
B)
{(–3, –1)}
C)
{(–4, –5)}
D)
{(–4, 4)}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
23)
y =2x + 4
4x + y =22
23)
A)
{(2, 8)}
B)
{(10, –18)}
C)
{(3, 10)}
D)
{(10, 3)}
Solve the system by the best method. Use set notation to express the solution set.
24)
x + y =6
y =2x
24)
A)
{(2, 4)}
B)
{(–2, 4)}
C)
{(–2, –4)}
D)
{(2, –4)}
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
25)
9x + 5y =51
7x – 2y =75
25)
A)
no solution;
B)
{(8, –5)}
C)
{(9, –5)}
D)
{(9, –6)}
Determine if the given ordered triple is a solution of the system.
26)
26)
(2, –3, 5)
x – y + z = – 6
x + y + z =4
x + y – z =0
A)
not a solution
B)
solution
10
Solve the problem.
27)
27)
A chemist needs 12 liters of a 50% salt solution. All she has available is a 20% salt solution and a
70% salt solution. How much of each of the two solutions should she mix to obtain her desired
solution?
A)
6 liters of the 20% solution; 6 liters of the 70% solution
B)
2.4 liters of the 20% solution; 9.6 liters of the 70% solution
C)
3.6 liters of the 20% solution; 8.4 liters of the 70% solution
D)
4.8 liters of the 20% solution; 7.2 liters of the 70% solution
Solve the system by the best method. Use set notation to express the solution set.
28)
y =3x + 5
4x + y =33
28)
A)
{(17, 4)}
B)
{(3, 14)}
C)
{(17, –35)}
D)
{(4, 17)}
Solve the system. If there is no solution or if the system’s equations are dependent, so state.
29)
3x +4y +z=14
5x –3y –z=12
5x +y+4z = – 3
29)
A)
no solution or
B)
{(3, –3, 2)}
C)
infinitely many solutions; dependent equations
D)
{(3, 2, –3)}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
30)
x + y = – 9
x – y =19
30)
A)
5, – 14
B)
9, – 14
C)
9, 5
D)
5, 14
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
31)
3x +1
4y = – 7
5x +1
3y = – 34
3
31)
A)
no solution;
B)
{(2, –5)}
C)
{(–1, –5)}
D)
{(–2, –4)}
Solve the problem.
32)
32)
Devon purchased tickets to an air show for 5 adults and 2 children. The total cost was $156. The
cost of a child’s ticket was $6 less than the cost of an adult‘s ticket. Find the price of an adult’s
ticket and a child’s ticket.
A)
adult’s ticket: $26; child’s ticket: $20
B)
adult’s ticket: $23; child’s ticket: $17
C)
adult’s ticket: $24; child’s ticket: $18
D)
adult’s ticket: $25; child’s ticket: $19
33)
33)
Sara invested $6600 in two stocks paying 10% and 9% annual interest, respectively. At the end of
the year, the total interest from these investments was $628. How much was invested at each
rate?
A)
$3400 at 10% and $3200 at 9%
B)
$6600 at 10% and $0 at 9%
C)
$3200 at 10% and $3400 at 9%
D)
$3300 at 10% and $3300 at 9%
34)
34)
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of
potato chips for $5.25. Another customer buys 4 hot dogs and 4 bags of potato chips for $9.00.
Find the cost of each item.
A)
$1.50 for a hot dog; $1.00 for a bag of potato chips
B)
$1.50 for a hot dog; $0.75 for a bag of potato chips
C)
$0.75 for a hot dog; $1.50 for a bag of potato chips
D)
$1.75 for a hot dog; $1.00 for a bag of potato chips
35)
35)
A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 4 hot dogs, 4 bags
of potato chips, and 4 soft drinks for $17.00. The price of a hot dog is $1.00 more than the price of
a bag of potato chips. The cost of a soft drink is $2.75 less than the price of two hot dogs. Find the
cost of each item.
A)
$2.00 for a hot dog; $1.00 for a bag of potato chips; $1.25 for a soft drink
B)
$1.00 for a hot dog; $2.00 for a bag of potato chips; $1.25 for a soft drink
C)
$2.25 for a hot dog; $1.25 for a bag of potato chips; $1.25 for a soft drink
D)
$2.00 for a hot dog; $1.25 for a bag of potato chips; $1.00 for a soft drink
36)
36)
Devon purchased tickets to an air show for 8 adults and 2 children. The total cost was $218. The
cost of a child’s ticket was $6 less than the cost of an adult‘s ticket. Find the price of an adult’s
ticket and a child’s ticket.
A)
adult’s ticket: $22; child’s ticket: $16
B)
adult’s ticket: $24; child’s ticket: $18
C)
adult’s ticket: $23; child’s ticket: $17
D)
adult’s ticket: $25; child’s ticket: $19
37)
37)
One number is four more than a second number. Two times the first number is 12 more than four
times the second number.
A)
2 and – 2
B)
3 and – 1
C)
– 10 and – 14
D)
1 and – 3
38)
38)
Julie and Eric row their boat (at a constant speed) 16 miles downstream for 2 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.
A)
5 mph
B)
4 mph
C)
3 mph
D)
2.5 mph
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
39)
x – 4 = y
y + 8 = x
39)
A)
no solution;
B)
{(4, 8)}
C)
{(8, 4)}
D)
infinitely many solutions; {(x, y) x – 4 = y} or {(x, y) y + 8 = x}
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
40)
4x + y = – 8
6x + 6y =6
40)
A)
{(–1, –4)}
B)
{(–3, 4)}
C)
{(3, 4)}
D)
{(–3, –4)}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
41)
–2x – 6y = – 3
4x +12y = 0
41)
A)
no solution;
B)
{(–3, 0)}
C)
infinitely many solutions; {(x, y) 4x +12y = 0} or {(x, y) –2x – 6y = – 3}
D)
{(0, –3)}
Solve the problem.
42)
42)
Molly has $12.45 in coins. She has four more nickels than dimes. She has seven fewer quarters
than dimes. How many quarters does she have?
A)
28 quarters
B)
32 quarters
C)
35 quarters
D)
39 quarters
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
43)
x + 4y = – 17
2x + 4y = – 18
43)
A)
{(1, –5)}
B)
no solution;
C)
{(0, –1)}
D)
{(–1, –4)}
44)
x + 7y =68
3x + 7y =78
44)
A)
{(6, 8)}
B)
no solution;
C)
{(–9, 5)}
D)
{(5, 9)}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
45)
9x + 4y =20
–2x – 2y = – 10
45)
A)
{(–1, 6)}
B)
no solution;
C)
{(0, 6)}
D)
{(0, 5)}
Solve the problem.
46)
46)
A bank loaned out $57,000, part of it at the rate of 11% per year and the rest at a rate of 7% per
year. If the interest received was $4990, how much was loaned at 11%?
A)
$32,000
B)
$25,000
C)
$26,000
D)
$31,000
47)
47)
Vicki’s car rental company charges $25 per day plus $0.25 per mile to rent a car. Joshua‘s rental
company charges $28 per day plus $0.20 per mile. The total daily cost, y, in dollars, of renting the
car if x miles are driven can be modeled by the linear system:
y = 0.25x +25 Vicki‘s
y = 0.20x +28 Joshua’s
Use graphing to solve the system. Interpret the coordinates of the solution in practical terms.
A)
{(60, 40)}; Both companies charge $40 for 60 miles driven.
B)
{(40, 35)}; Both companies charge $35 for 40 miles driven.
C)
{(60, 45)}; Both companies charge $45 for 60 miles driven.
D)
{(60, 40)}; Both companies charge $60 for 40 miles driven.
48)
48)
Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual interest,
and the remainder in a mutual fund that paid 11% annual interest. If his total interest for that
year was $800, how much did Kevin invest in the mutual fund?
A)
$5000
B)
$6000
C)
$3000
D)
$4000
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
49)
7x + 5y = – 20
3x + 3y = – 12
49)
A)
{(0, –3)}
B)
no solution;
C)
{(0, –4)}
D)
{(–1, –3)}
Determine if the given ordered triple is a solution of the system.
50)
50)
(–4, 2, –1)
x – y + z = – 7
x + y + z = – 3
x + y – z = – 1
A)
solution
B)
not a solution
Determine whether the ordered pair is a solution of the system.
51)
51)
(–2, –2)
2x + y = – 2
3x + 2y = – 2
A)
Yes
B)
No
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
52)
x – 7y = – 1
2x – 6y = – 2
52)
A)
{(0, –1)}
B)
{(–1, 0)}
C)
{(1, –1)}
D)
no solution;
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
53)
x + y =7
x – y =1
53)
A)
{(–4, 4)}
B)
{(4, 3)}
C)
no solution;
D)
{(3, 4)}
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
54)
y = 0
y = – 5
54)
A)
no solution;
B)
infinitely many solutions; {(x, y) y = – 5} or {(x, y) y = 0}
C)
{(–5, 0)}
D)
{(0, –5)}
55)
y – 4x =2
6y =24x + 12
55)
A)
{(1, 1)}
B)
{(–1.5, –1)}
C)
infinitely many solutions; {(x, y) y – 4x =2} or {(x, y) 6y =24x + 12}
D)
no solution;
Solve the problem.
56)
56)
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of
potato chips for $6.25. Another customer buys 3 hot dogs and 5 bags of potato chips for $9.75.
Find the cost of each item.
A)
$0.75 for a hot dog; $2.00 for a bag of potato chips
B)
$2.00 for a hot dog; $0.75 for a bag of potato chips
C)
$2.00 for a hot dog; $1.00 for a bag of potato chips
D)
$2.25 for a hot dog; $1.00 for a bag of potato chips