Question : Doreen and Irena plan to leave their houses at the same time : 2158614
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.
81) One number is four more than a second number. Two times the first number is 12 more than four times the second number.
A) 3 and - 1
B) 2 and - 2
C) - 10 and - 14
D) 1 and - 3
82) 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: $ 23; child's ticket: $ 17
C) adult's ticket: $ 25; child's ticket: $ 19
D) adult's ticket: $ 24; child's ticket: $ 18
83) Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 5 times as many dimes as nickels, and the value of the dimes is $2.70 more than the value of the nickels. How many nickels and dimes does Jamil have?
A) 5 nickels and 25 dimes
B) 6 nickels and 30 dimes
C) 7 nickels and 35 dimes
D) 30 nickels and 6 dimes
84) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $11 each and a number of necklaces at $14 each. She wrote a check for $1590 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?
A) 30 bracelets and 90 necklaces
B) 35 bracelets and 85 necklaces
C) 25 bracelets and 95 necklaces
D) 40 bracelets and 80 necklaces
85) 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; $ 1.00 for a bag of potato chips
C) $ 2.00 for a hot dog; $ 0.75 for a bag of potato chips
D) $ 2.25 for a hot dog; $ 1.00 for a bag of potato chips
86) The three angles in a triangle always add up to 180°. If one angle in a triangle is 56° and the second is 3 times the third, what are the three angles?
A) 56°, 93°, 31°
B) 56°, 91°, 33°
C) 56°, 94°, 30°
D) 56°, 92°, 32°
87) Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 3 times the width. He needs 50 feet of fencing to do the job. Find the length and width of the garden.
A) length: 24 feet; width: 5 feet
B) length: 18 feet; width: 3 feet
C) length: 21 feet; width: 4 feet
D) length: 393/4feet; width: 101/4feet
88) 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?
89) How can $28,000 be invested, part at 4% annual interest and the remainder at 10% annual interest, so that the interest earned by the two accounts is equal at the end of the year?
A) $18,000 invested at 4%; $10,000 invested at 10%
B) $10,000 invested at 4%; $18,000 invested at 10%
C) $8000 invested at 4%; $20,000 invested at 10%
D) $20,000 invested at 4%; $8000 invested at 10%
90) Melissa invested a sum of money at 3% annual interest. She invested three times that sum at 5% annual interest. If her total yearly interest from both investments was $5400, how much was invested at 3%?
91) If $2000 is invested at 10% annual interest, how much should be invested at 12% annual interest so that the total yearly income from both investments is $5000?
92) 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) $40,000 in B-rated bonds and $29,000 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) $30,000 in B-rated bonds and $39,000 in a CD
93) 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%?
94) 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?
95) A college student earned $7000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 9%. If the student received a total of $656 in interest at the end of the year, how much was invested at 10%?
96) A retired couple has $ 160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $ 15,600 per year?
A) $ 120,000 at 11% and $ 40,000 at 6%
B) $ 110,000 at 6% and $ 50,000 at 11%
C) $ 130,000 at 11% and $ 30,000 at 6%
D) $ 120,000 at 6% and $ 40,000 at 11%
97) How much pure acid should be mixed with 4 gallons of a 50% acid solution in order to get an 80% acid solution?
A) 10 gal
B) 16 gal
C) 6 gal
D) 2 gal
98) 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) 2.4 liters of the 20% solution; 9.6 liters of the 70% solution
B) 3.6 liters of the 20% solution; 8.4 liters of the 70% solution
C) 4.8 liters of the 20% solution; 7.2 liters of the 70% solution
D) 6 liters of the 20% solution; 6 liters of the 70% solution
99) The radiator in a certain make of car needs to contain 40liters of 40% antifreeze. The radiator now contains 40liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze to get the desired strength?
A) 20 liters
B) 16 liters
C) 13.3 liters
D) 10.0 liters
100) 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) 39 pounds
B) 42 pounds
C) 48 pounds
D) 45 pounds
101) The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $11 per pound. How many pounds of the $6 coffee should be used?
A) 144 pounds
B) 72 pounds
C) 54 pounds
D) 27 pounds
102) The manager of a candy shop sells chocolate covered peanuts for $5 per pound and chocolate covered cashews for $15 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew-peanut mixture that will sell for $11 per pound. How many pounds of peanuts should be used?
A) 20 pounds
B) 25 pounds
C) 50 pounds
D) 10 pounds
103) Jimmy is a partner in an Internet-based coffee supplier.The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $6 per pound. Jimmy is creating a medium-price product that will sell for $8 per pound.The first thing to go into the mixing bin was 10 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?
A) 31 pounds
B) 29 pounds
C) 30 pounds
D) 32 pounds
104) Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $ 64.85. How many dimes did she deposit?
A) 429 dimes
B) 863 dimes
C) 439 dimes
D) 434 dimes
105) 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) 39 quarters
B) 35 quarters
C) 28 quarters
D) 32 quarters
106) A newspaper carrier has $12.80 in change. He has two more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he have?
A) 78 quarters, 76 dimes, 26 nickels
B) 26 quarters, 28 dimes, 78 nickels
C) 28 quarters, 26 dimes, 84 nickels
D) 26 quarters, 24 dimes, 78 nickels
107) 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) 7 hundreds, 3 twenties, 12 fives
B) 9 hundreds, 2 twenties, 8 fives
C) 8 hundreds, 2 twenties, 16 fives
D) 7 hundreds, 2 twenties, 16 fives
108) 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) 2.5 mph
D) 3 mph
109) A twin-engined aircraft can fly 1360 miles from city A to city B in 5 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?
A) 34 mph
B) 68 mph
C) 85 mph
D) 51 mph
110) 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) 8 hours
C) 5 hours
D) 32 hours
111) Khang and Hector live 27 miles apart in southeastern Missouri. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is 80% of Khang's. They start out at the same time and meet 3 hours later. Find Hector's rate of speed.
A) 27 mph
B) 5 mph
C) 4 mph
D) 15 mph
112) 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) 10.08 miles
D) 18 miles