Determine if the given ordered triple is a solution of the system.
92)
92)
(5, –1, 1)
x + y + z =5
x – y + 4z =10
5x + y + z =25
A)
not a solution
B)
solution
Solve the problem.
93)
93)
Doreen and Irena plan to leave their houses at the same time, roller blade towards each other,
and meet for lunch after 3 hours on the road. Doreen can maintain a speed of 2.4 miles per hour,
which is 40% of Irena’s speed. If they meet exactly as planned, what is the distance between their
houses?
A)
7.2 miles
B)
25.2 miles
C)
18 miles
D)
10.08 miles
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.
94)
x + y = – 4
y =3x
94)
A)
{(1, 3)}
B)
{(–1, 3)}
C)
{(1, –3)}
D)
{(–1, –3)}
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.
95)
4x =8y + 9
4x =8y – 4
95)
A)
0, –9
8
B)
1
8, 1
16
C)
{(8, 9)}
D)
no solution;
Solve the problem.
96)
96)
Keema cashed her paycheck and came home from the bank with $820 in bills of the following
denominations: twenties, fives, and hundreds. She has eight times as many fives as twenties and
five more hundreds as twenties. How many of each denomination does she have?
A)
8 hundreds, 2 twenties, 16 fives
B)
7 hundreds, 2 twenties, 16 fives
C)
7 hundreds, 3 twenties, 12 fives
D)
9 hundreds, 2 twenties, 8 fives
Determine if the given ordered triple is a solution of the system.
97)
97)
(4, 5, –1)
3x + 3y + z =16
5x – 4y – z = – 29
3x + y + 5z =22
A)
solution
B)
not a solution
Solve the system. If there is no solution or if the system‘s equations are dependent, so state.
98)
x+3y +3z =1
3y +2z = – 6
z=3
98)
A)
no solution or
B)
{(4, 3, –4)}
C)
{(4, –4, 3)}
D)
infinitely many solutions; dependent equations
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.
99)
4x + y =12
16x + 4y =48
99)
A)
no solution;
B)
{(0, 12)}
C)
{(5, –8)}
D)
infinitely many solutions; {(x, y) 4x + y =12} or {(x, y) 16x + 4y =48}
Solve the problem.
100)
100)
Ron attends a party. He wants to limit his food intake to 140 g protein, 125 g fat, and 153 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?
A)
5 mushrooms; 4 meatballs; 6 eggs
B)
4 mushrooms; 6 meatballs; 5 eggs
C)
6 mushrooms; 5 meatballs; 4 eggs
D)
7 mushrooms; 6 meatballs; 5 eggs
101)
2x – 2y =10
101)
A)
{(1, 6)}
B)
no solution;
C)
{(6, 1)}
D)
{(3, 4)}
Solve the problem.
102)
102)
How much pure acid should be mixed with 4 gallons of a 50% acid solution in order to get an 80%
acid solution?
A)
2 gal
B)
16 gal
C)
6 gal
D)
10 gal
Determine if the given ordered triple is a solution of the system.
103)
103)
(–3, 3, 0)
x – y + 3z = – 12
4x + z = – 3
x + 4y + z =9
A)
solution
B)
not a solution
Solve the problem.
104)
104)
Ms. Adams received a bonus check for $12,000. 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 $500,
how much was placed in each account?
A)
municipal bond: $1500
certificate of deposit: $3000
money market: $7500
B)
municipal bond: $2000
certificate of deposit: $4000
money market: $6000
C)
municipal bond: $2500
certificate of deposit: $5000
money market: $4500
D)
municipal bond: $1750
certificate of deposit: $3500
money market: $6750
105)
105)
A barge takes 2 hours to move (at a constant rate) downstream for 16 miles, helped by a current
of 3 miles per hour. If the barge‘s engines are set at the same pace, find the time of its return trip
against the current.
A)
2 hours
B)
32 hours
C)
8 hours
D)
5 hours
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.
106)
2x – y = – 8
y=2
106)
A)
no solution;
B)
{(–3, 2)}
C)
{(3, –2)}
D)
{(2, –3)}
Solve the system. If there is no solution or if the system‘s equations are dependent, so state.
107)
x–y+5z =5
3x +z=0
–x+y–5z = – 25
107)
A)
{(0, 0, –5)}
B)
infinitely many solutions; dependent equations
C)
no solution or
D)
{(5, –5, 0)}
Solve the problem.
108)
108)
Don James wants to invest $69,000 to earn $4210 per year. He can invest in B–rated bonds paying
9% per year or in a Certificate of Deposit (CD) paying 4% per year. How much money should be
invested in each to realize exactly $4210 in interest per year?
A)
$30,000 in B–rated bonds and $39,000 in a CD
B)
$29,000 in B–rated bonds and $40,000 in a CD
C)
$39,000 in B–rated bonds and $30,000 in a CD
D)
$40,000 in B–rated bonds and $29,000 in a CD
109)
109)
The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate–covered
raisins, which usually sells for $3 per pound, and chocolate–covered macadamia nuts, which
usually sells for $8 per pound. They have a 30–pound barrel of the raisins. How many pounds of
the nuts should they mix with the barrel of raisins so that they hit their target value of $6 per
pound for the mixture?
A)
45 pounds
B)
48 pounds
C)
39 pounds
D)
42 pounds
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.
110)
1
2x – y = 1
x =2
110)
A)
{(2, 1)}
B)
{(2, 0)}
C)
{(0, 2)}
D)
2, 1
2
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.
111)
x +5
3=y +19
6
x
2=2y +8
4
111)
A)
no solution;
B)
infinitely many solutions; (x, y) x +5
3=y +19
6 or (x, y) x
2=2y +8
4
C)
{(1, 5)}
D)
{(5, 1)}
Solve the system. If there is no solution or if the system‘s equations are dependent, so state.
112)
8x –8y +5z =69
–24x +24y –15z = – 207
16x –16y +10z =138
112)
A)
no solution or
B)
{(–2, 9, –5)}
C)
infinitely many solutions; dependent equations
D)
{(–2, –5, 9)}
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.
113)
2x + 10y = – 64
9x + 2y =56
113)
A)
{(–2, 8)}
B)
{(–8, 8)}
C)
{(8, –8)}
D)
{(9, –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.
114)
y =5x + 4
y =8x + 3
114)
A)
17
3, 1
3
B)
infinitely many solutions; {(x, y) y =5x + 4} or {(x, y) y =8x + 3}
C)
no solution;
D)
1
3, 17
3
Solve the problem.
115)
115)
Three trains one eastbound, one westbound, and one northbound leave a city at the same
time. The speed of the northbound train is 30 miles per hour greater than the speed of the
eastbound train. After 6 hours, the distance between the westbound train and the eastbound train
is 420 miles. Twice the speed of the westbound train is 20 miles per hour more than the speed of
the northbound train. Find the speeds of the three trains.
A)
eastbound, 60 mph; westbound, 40 mph; northbound, 30 mph
B)
eastbound, 40 mph; westbound, 40 mph; northbound, 70 mph
C)
eastbound, 20 mph; westbound, 50 mph; northbound, 60 mph
D)
eastbound, 30 mph; westbound, 40 mph; northbound, 60 mph
Determine whether the system is inconsistent, dependent, or neither.
116)
4x + y – 3z =15
–x – 2y + 2z = – 11
–9x – 4y + 8z = – 41
116)
A)
neither
B)
inconsistent
C)
dependent
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.
117)
–7x + 9y = – 21
–4x – 2y = – 12
117)
A)
{(2, 1)}
B)
{(3, 0)}
C)
{(3, 1)}
D)
no solution;
Solve the problem.
118)
118)
One number is 5 less than a second number. Twice the second number is 5 less than 5 times the
first. Find the two numbers.
A)
5 and 10
B)
6 and 11
C)
4 and 9
D)
–10 and –5
119)
119)
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3
hours to prepare, 2 hours to paint, and 9 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, 13 hours to paint, and 7 hours to fire.
If the workshop has 95 hours for prep time, 56 hours for painting, and 111 hours for firing, How
many of each can be made?
A)
4 wreaths, 2 trees, 9 sleighs
B)
9 wreaths, 4 trees, 2 sleighs
C)
2 wreaths, 9 trees, 4 sleighs
D)
10 wreaths, 5 trees, 3 sleighs
120)
120)
Two numbers total 12, and their difference is 16. Find the two numbers.
A)
7 and 5
B)
12 and 2
C)
6 and – 10
D)
14 and – 2
121)
121)
A chemist needs to mix a 20% acid solution with a 70% acid solution to obtain 7 liters of a 50%
acid solution. How many liters of each of the solutions must be used?
A)
2.8 L of the 20% solution; 4.2 L of the 70% solution
B)
1.4 L of the 20% solution; 5.6 L of the 70% solution
C)
2.1 L of the 20% solution; 4.9 L of the 70% solution
D)
3.5 L of the 20% solution; 3.5 L of the 70% solution