Problem # 1 - 5 points
The sum of two numbers is 231. The larger is twice the smaller. What are the numbers?

Problem #2 - 5 points
The length of a rectangle is three times the width. If the perimeter is 80 feet, what are the dimensions?

Problem #3 - 5 points
The length of a rectangle is six less than twice the width. If the perimeter is 60 inches, what are the dimensions?

Problem #4 - 5 points
A man earns $1000 more than three times what his son earns. If the total amount of what they both earn is $29,000, how much money did the father and son each earn?

Problem #5 - 5 points
A piece of wire 60 inches long is cut into two pieces so that the larger piece is 10 inches longer than the shorter piece. How long is each piece of wire?

Problem # 6 - 10 points
Two tuna boats start from the same port at the same time, but they head in opposite directions. The faster boat travels 10 knots per hour faster than the slower boat. At the end of eight hours, they were 272 nautical miles apart. How many nautical miles had each boat travelled by the end of the eight hour period?

Problem #7 - 5 points
In an algebra class there are 10 less than twice as many boys as girls. If the total number of students is 38, how many boys and girls are in the class?

Problem # 8 - 5 points
The cost of a bottle and a cork is $1.10. If the bottle costs $1.00 more than the cork, what is the cost of each?

Problem #9 - 10 points
A man's will left $75,000 to his wife, son, and daughter in a way such that his son's share was 3 times the daughter's share, while the wife received as much as the son and the daughter together. How much did each receive?

Problem #10 - 10 points
A 747 and 727 leave the same airport at the same time and travel in opposite directions at 600 mph and 450 mph, respectively. In how many hours will they be 3,150 miles apart?

Problem #11 - 10 points
A helicopter travelling at an average rate of 150 mph left from a downtown terminal at noon after a train which had departed from the same terminal at 9 am. If the helicopter overtook the train at 2 pm, find the average speed of the train.

Problem #12 - 10 points
Two cars 720 kilometers apart travel toward each other. One car travels 70 kph while the other travels at 50 kph. In how many hours will they meet?

Problem #13 - 10 points
Two boys on bicycles start from the same place at the same time. One cyclist travels 15 mph, the other at 12 mph. If they travel in the same direction, how many hours will it take before they are 9 miles apart?

Problem #14 - 10 points
A plane leaves St. Louis at 10 am flying north. Another plane from the same airport flies south at 12 pm. At 2 pm they are 1800 miles apart. Find the rate of speed of each plane if the rate of the plane flying north is twice that of the plane flying south.

Problem # 15 - 10 points
A freight train takes 18 hours to travel the same distance that an express train travels in 15 hours. The rate of the express is 15 mph faster than the freight train. Find the rate at which each train travels.

Problem # 16 - 10 points
At 10 am two classmates start out on their bikes to meet each other from towns located 68 miles apart. At 1 pm they meet. If one boy traveled 3 mph faster than the other, what was the rate of speed of each boy?

Problem #17 - 10 points
At 12 noon two Mississippi steam boats are 126 miles apart. At 6 pm, they pass each other going in opposite directions. If one steam boat travels nine mph faster than the other, find the speed of both boats.

Problem #18 - 10 points
A jet bomber traveling 500 mph arrived over its target at the same time as its fighter jet escort which left the same base 1/2 hour later. How many hours did it take to reach the target if the fighter jet traveled at 600 mph?

Problem # 19 - 10 points
A private jet had been flying for two hours when it encountered strong head winds which reduced its speed by 40 mph. If it took the plane 5 hours to travel 1,380 miles, find its speed before flying into the headwinds.

Problem #20 - 5 points
In a collection of coins that has a value of $4.90, there are 20 more nickels than dimes. How many nickels and dimes are there in the collection?

Problem #21 - 5 points
A student at Ellwood High School has a collection of quarters and nickels amounting to $18.70. If there are 20 more nickels than quarters, how many of each kind of coin does the student have?

Problem #22 - 10 points
A woman has $10.50 in change consisting of twice as many half dollars as quarters and five times as many dimes as quarters. How many half dollars, quarters, and dimes does she have?

Problem #23 - 10 points
Sylvia has $11.25 in nickels, dimes, and quarters. She has three times as many nickels as dimes and 5 more quarters than dimes. How many of each kind of coin does she have?

Problem # 24 - 10 points
A news boy collected $68.50 on his paper route one week. The collection consisted of nickels, dimes, and quarters. If he had 70 more nickels than quarters, and twenty more dimes than nickels, how many of each coin did he have?

Problem # 25 - 5 points
Eighty-six coins made up of dimes and quarters amount to $14.60. How many of each of these coins are there?

Problem # 26 - 10 points
A piggy bank contained 110 coins including nickels, dimes, and quarters. If there are 20 more nickels than quarters, and the number of dimes is equal to the number of quarters, how many of each kind of coin are there if the total collection is $13.00?

Problem #27 - 10 points
A high school play grossed $122.50. If there were twice as many student tickets sold as there were adult tickets sold, and if each student ticket sold for 50 cents and each adult ticket sold for 75 cents, how many student and how many adult tickets were sold for the play?

Problem # 28 - 10 points
Ralph, who is president of the senior class, sold $67.50 worth of tickets for the music festival. If he sold 20 more student tickets than adult tickets, and the cost for student tickets was 75 cents and adult tickets $1.00, how many of each kind of ticket did he sell?

Problem # 29 - 10 points
Susie bought $5.61 worth of stamps. She bought the same number of 2 and 5 cent stamps and double that number of 22 cent stamps. How many of each kind of stamp did she buy?

Problem #30 - 10 points
To reduce 32 grams of a 25% solution of antiseptic to a 10% solution, how much distilled water should a pharmacist add?

Problem #31 - 10 points
How many liters of a 20% solution of acid should be added to 10 liters of a 30% solution of acid to contain a 25% solution?

Problem #32 - 10 points
How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a 40% solution of acid?

Problem # 33 - 10 points
A chemist has a solution of 50% pure acid and another of 80% pure acid. How many gallons of each will make 660 gallons of 72% acid?

Problem # 34 - 10 points
How much alcohol must be added to 1 quart of tincture of arnica containing 20% arnica to reduce it to a 10% arnica solution?

Problem #35 - 10 points
How many quarts of peanut oil worth 19 cents a quart must be mixed with 100 quarts worth 25 cents a quart to produce a mixture which will sell for 24 cents?

Problem #36 - 10 points
A storekeeper wishes to sell 100 pounds of mixed nuts at $1.75 a pound. He mixes nuts worth $1.65 a pound with cashews worth $1.90 a pound. How many pounds of each does he use?

Problem #37 - 10 points
A merchant wishes to blend 200 pounds of coffee worth $3.20 a pound from two mixtures. One at #3.00 per pound and the other at $3.25 per pound. How many pounds of each mixture should he use?

Problem # 38 - 10 points
A grocer has two kinds of tea. One selling for 80 cents per pound and the other for 60 cents a pound. How many pounds of each must he use to make 50 pounds at 74 cents a pound?

Problem # 39 - 10 points
A dairy wishes to mix 1,000 pounds of milk containing 8% butterfat. If the mixture is to be made from milk containing 5% butterfat and cream containing 20% butterfat, how many pounds of each is needed?

Problem # 40 - 10 points
How many ounces of an alloy containig 30% gold on the world market must be mixed with an alloy containing 5% gold to obtain 25 ounces of an alloy containig 20% gold?

Problem # 40 - 10 points
A pharmacist has 12% solution and a 20% solution of boric acid. How much of each must he use to make 80 grams of a 15% solution?

Problem # 42 - 10 points
A druggist has a 18% solution of argyol. How much of this solution and how much water must be mixed together to make 10 liters of a 12% solution?

Problem # 43 - 10 points
A grocer wishes to blend two different coffee brands. He wants to make a blend of 480 pounds to sell at $2.68 per pound. If he uses a blend of coffee worth $2.50 a pound with another worth $2.80 a pound, how many pounds of each does he use?

Problem # 44 - 10 points
How many ounces of iodine worth 30 cents an ounce must be mixed with 50 ounces of iodine worth 18 cents an ounce so that the mixture an be sold for 20 cents an ounce?

Problem #45 - 10 pointa
How many gallons of rocket fuel containing 80% liquid oxygen must be mixed wth 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen?

Problem #46 - 10 points
The winery's tastiest wine must contain 12% alcohol content. How many gallons of wine with 9% alcohol must be mixed with 3,000 gallons of wine with 15% alcohol content in order to achieve the desired 12% alcohol content?

Problem #47- 10 points
The Davidson winery is noted for its Regal champagne. It takes a blending of 1,000 bushels of a mixture of two varieties of grapes to achieve the Regal specification of 12% alcohol content for its champagne. One of its two varieties of grapes contains a 10% alcohol content and the other a 15% content. How many bushels of each variety are needed?

Problem # 48 - 10 points
The capacity of a car radiator is 20 quarts. If it is full of a 55% antifreeze solution, how many quarts must be drained off and replaced by a 80% solution to give 20 quarts of a 70% solution?

Problem # 49 - 10 points
The capacity of a car radiator is 18 quarts. If it is full of a 20% antifreeze solution, how many quarts must be drained off and replaced by a 100% solution to give 18 quarts of a 39% solution?

Problem # 50 - 5 points
Four brothers decided to buy a color television set that cost $392. Their contributions were in the ratio 4:2:3:5. How much did each contribute?

Problem #51 - 10 points
Marie and Tony went shopping together. Marie bought 2 L of milk and 10 oranges for $3.44. Tony bought 3 L of milk and 8 oranges for $3.69. What was the cost of 1 L of milk? One orange?

Problem #52 - 10 points
The hypotenuse of a right triangle is 3 cm longer than twice the length of the shorter leg. The longer leg measures 12 cm. Find the lengths of the shorter leg and the hypotenuse.

Problem #53 - 10 points
Card reader A can read decks of punched cards in half the time it takes Card reader B. Together they can read a certain deck in 8 minutes. How long would it take each reader alone to read the deck?

Problem #54 - 10 points
How many grams of 5% antiseptic solution must be added to 300 grams of a 10% solution to produce an 8% solution?

Problem # 55 -10 points
Anthony has $6.10 in coins. He has 6 more quarters than nickels and half as many dimes as quarters. He also has three half dollars. How many coins of each type does he have?

Problem #56 5 points
John Kennedy's picture appears on 8% of Pedro's collection of presidential campaign buttons. If he has 34 Kennedy buttons, how many buttons has he in all?

Problem # 57 - 5 points
Two years ago Seth was one third as old as his father. If he is now 22 years younger than his father, how old is Seth now?

Problem #58 - 10 points
A square and a rectangle have the same area. If the length of the rectangle is 4 cm greater and the width is 3 cm less than the length of a side of the square, what are the dimensions of the rectangle?

Problem #59 - 10 points
Colin and Maureen receive $3.50/h and $4.00/h, respectively for working in Brenda's garden. Colin works on Saturday's and Maureen works on Sunday's. How much money did each one earn if they received $42 between them for a total of 11 hours of work one weekend?

Problem #60 - 10 points
The ratio of the lengths of the sides of two squares is 3:7. The sum of their areas is 522 square cm. Find the area of each square.

Problem #61 - 10 points
Find the three smallest consecutive odd integers whose sum is at least 99.

Problem # 62 - 15 points
The volume of a cylinder varies directly as the square of the radius of the base. If the volume is 18cm cubed whan the radius is 3 cm, find the volume when the radius is 4 cm.

Problem #63 - 10 points
Heather paid $650 for some stock in Newcar, Inc. If she sold the stock for $728, what was the percent gain on her oriinal investment?

Problem #64 - 10 points
The width of a rectangle is 5 cm less than half its length. Its area is 72 sq cm. Find the length and the width of the rectangle.

Problem #65 - 10 points
The denominator of a fraction is 1 more than twice the numerator. If 1 is subtracted from the numerator, the resulting fraction is equivalent to 1/3. Find the original fraction.

Problem #66 - 10 points
The first cyclist in a two-leg relay race rode at a speed of 40 km/h. The second cyclist rode at 30 km/h. If they completed the 170 km course in 4 h 50 min, how far did each ride?

Problem #67 - 10 points
A sample quilt is made from 150 small squares. It is possible to make a quilt of the same size using 100 squares, 1 cm longer on each side than the smaller squares. What is the length of a side of each smaller square?

Problem #68 - 10 points
Inge invested part of her $6000 savings in common stock and the rest in rare stamps. At the end of the year, she realized a gain of 9% on the stocks and 12% on the stamps. If her saving account is now $6615, how much did she invest in stamps?

Problem # 69 - 15 points
A 3m by 5m rectanglular wall hanging is hung in the center of a wall. The uncovered part of the wall is a border strip with uniform width. How wide is the border strip if the area of the wall hanging is three sevenths the area of the entire wall?

Problem #70 - 10 points
A tea merchant prepares a blend of 30 kg of tea to sell at $2.95/kg. The merchant blends two types of tea, one selling at $2.70/kg, the other at $3.00/kg. How much of each type should the merchant use?

Problem #71 - 10 points
The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 7 more than twice the original number. Find the original number.

Problem #72 - 10 points
Paula leaves her house at 1:20 pm to get to the ball park by 2:00 pm. Malcolm leaves his house for the ball park at 1:30 pm. Paula lives 2 km farther away from the ball park than Malcolm, but can walk 2 km/h faster. How fast can Paula walk?

Problem #73 - 10 points
A boat can travel 6 km downstream in 40 min. The return trip takes one hour. Find the rate of the boat in still water and the rate of the current.

Problem #74 - 10 points
On her birthday, Jane received $1000. If she invested the money in two banks, one paying 6% interest and the other 7%, how much did she invest in each bank if her annual interest was $65?

Problem #75 - 10 points
Part of $12000 is invested in 9% bonds and the remainder in common stocks paying 8%. If the yearly income from both investments is $1040, how much was invested in bonds and how much was invested in stocks?

Problem #76 - 10 points
A newly married couple has $4200 to invest. If they invest in one real estate mortgage paying 9.5% and another paying 9%, how much did they invest in each mortgage if their yearly earnings are $392?

Problem #77 - 10 points
Ralph's uncle invested $1000 more in a 6% investment than in a 5% investment. If his yearly income from both investments is$1710, how much did he invest at each rate?

Problem #78 - 10 points
Mrs. Walsh has $14000 to invest. She chooses two investments, one paying 8.5% and one paying 7.5%,. If her yearly earnings from both investments is $1152, what did she invest in 8.5%?

Problem #79 - 10 points
Mr. Camp invested twice as much in a savings account at 6.5% as he invested in a note at 7%. If his yearly income from both investments is $800, how much is invested at 6.5% and at 7%?

Problem #80 - 10 points
Mrs. Chin, on reaching age 65, invested $18000 of her insurance policy in bonds paying 8.5% and a stock paying 7.5%. If her yearly income from these two is $1470, how much did she invest in the bonds and how much in the stocks?

Problem #81 - 10 points
Two investments produce a $150 income each month. If $1000 more is invested at 9% than 10%, how much is invested at each percent?

Problem #82 - 10 points
A man had $12000 to invest. If his income from a savings account earning 7.5% is $280 greater than his income from another investment at 8%, how much did he invest at each rate?

Problem #83 - 10 points
Two sums of money differing by $2000 were invested, the larger at 8.5% and the smaller at 9.5%. If the larger sum yielded an annual income that was $110 more than the other, how much money was invested at each rate?

Problem #84 - 10 points
Mr. Rockford invested a certain amount of money at 8.5%, but then invested $600 more at 7.5%. If his total income from both investments is $4421, what amount was invested at each rate?

Problem #85 - 10 points
Mrs. Roberts invested $1500 less at 9% than at 8%. If the income from the smaller investment is $95 less than the income from the larger investment, how much did he invest at 9% and at 8%?

Problem #86 - 15 points
Three investments yield $1965. The amount invested at 9% is $1500 more than at 8%. The amount invested at 10% is $500 less than three times the amount invested at 8%. How much is invested 8%, 9%, and 10%.

Problem #87 - 10 points
It takes Mr. Rose 10 hours to complete a printing job. His helper John can complete the same job in 15 hours. If Mr. Rose and John work together, how long will take them to complete the job?

Problem #88 - 10 points
It takes one machine 25 minutes to pick a bale of cotton and another machine 30 minutes. If both machines are used, how long will it take them to pick a bale of cotton?

Problem #89 - 10 points
A tank can be filled by one pump in 50 minutes and by another in 60 minutes. A third can drain the tank in 75 minutes. If all three pumps go into operation, how long will it take to fill the tank?

Problem #90 - 10 points
A gardener can care for the Green's property in 5 hours. If his helper assists him, they can complete the job in 4 hours. How long will it take the helper to do the job alone?

Problem #91 - 10 points
Walter, Bill, and Tom want to decorate the Gym for a school dance. It would take Walter and Bill 4 hours each to do the job and Tom alone could do the job in 3 hours. If they all work together, how long will it take them to decorate the Gym?

Problem #92 - 10 points
Nancy can do a typing job in 8 hours. When Carol helps her, the can do the job in 5 hours. How many hours will it take Carol to do the job alone?

Problem #93 - 10 points
Mr. Sharon can paper a room in 3 hours. His assistant needs 5 hours. If Mr. Sharon works one hour and then his assistant completes the job alone, how long will it take the assistant to finish the job?

Problem #94 - 10 points
Mr. Smith, a college instructor, can grade papers in 3 hours while it takes his assistant 4.5 hours. If Mr. Smith graded the papers for 1 hour and then left the job for his assistant, how long will it take the assistant to finish grading?

Problem #95 - 10 points
It takes 8 hours for one crew to clean an office buliding. It takes a second crew 10 hours. If the first crew works 2 hours and leaves for the second crew to take over, how long will it take the second crew to finish?

Problem #96 - 10 points
Mr. Ito's assistant takes twice as long to complete a computer task as Mr. Ito. If it takes both 6 hours to complete the task, how long will it take each of them to do the job alone?

Problem #97 - 10 points
Mr. Vella can build a brick wall in 4 days. His apprentice can build the same wallin 6 days. After working alone for 3 days, Mr. Vella became ill and left the job for his apprentice to complete. How many days did it take the apprentice to finish?