1. Find the value of two numbers if their sum is 12 and their difference is 4.


 Jeffery Osborne
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1 1. Find the value of two numbers if their sum is 12 and their difference is The difference of two numbers is 3. Their sum is 13. Find the numbers. 3. Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air. 4. The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket. 5. The sum of the digits of a certain twodigit number is 7. Reversing its digits increases the number by 9. What is the number? 6. A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current? 7. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. 8. The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? 9. Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket? 10. Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges. 11. A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current? 12. DeShawn and Shayna are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs. DeShawn sold 10 bags of windflower bulbs and 12 bags of daffodil bulbs for a total of $380. Shayna sold 6 bags of windflower bulbs and 8 bags of daffodil bulbs for a total of $244. What is the cost each of one bag of windflower bulbs and one bag of daffodil bulbs? 1
2 1. Ten grams of sugar are added to a 40 g serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mixture? grams in bowl % sugar total grams sugar sugar 10 cereal mix? 2. Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters of another punch. The resulting fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch. liters punch % juice total liters juice 35% juice 200 other punch 300 x mix 3. How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 pounds of corn that costs $0.50 per pound to make a mixture of vegetables that costs $0.65 per pound? lima beans corn mix pounds $/pound total $ for veggies x 4. Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound. pounds coffee $/pound total $ for coffee pricey cheapo mix? 5. How many ounces of pure water must be added to 50 ounces of a 15% saline solution to make a saline solution that is 10% salt? ounces liquid % salt total ounces salt water x 15% solution 10% mix 6. How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution? liters solution % alcohol total liters alcohol 70% solution x 40% solution 50% mix 7. Twentysix coins in a pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin do we have? number of coins cents per coin total cents quarters q 25 dollars total 26 2
3 1. A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and onehalf as many dimes as nickels, how many coins of each kind are there? 2. A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain? 3. 2 m 3 of soil containing 35% sand was mixed into 6 m 3 of soil containing 15% sand. What is the sand content of the mixture? 4. 9 lb. of mixed nuts containing 55% peanuts were mixed with 6 lb. of another kind of mixed nuts that contain 40% peanuts. What percent of the new mixture is peanuts? 5. 5 fl. oz. of a 2% alcohol solution was mixed with 11 fl. oz. of a 66% alcohol solution. Find the concentration of the new mixture lb of Brand M Cinnamon was made by combining 12 lb of Indonesian cinnamon which costs $19/lb with 4 lb of Thai cinnamon which costs $11/lb. Find the cost per lb of the mixture. 7. Emily mixed together 9 gal. of Brand A fruit drink and 8 gal. of Brand B fruit drink which contains 48% fruit juice. Find the percent of fruit juice in Brand A if the mixture contained 30% fruit juice. 8. How many mg of a metal containing 45% nickel must be combined with 6 mg of pure nickel to form an alloy containing 78% nickel? 9. How much soil containing 45% sand do you need to add to 1 ft 3 of soil containing 15% sand in order to make a soil containing 35% sand? gal. of a sugar solution was mixed with 6 gal. of a 90% sugar solution to make a 84% sugar solution. Find the percent concentration of the first solution. 11. A metallurgist needs to make 12.4 lb. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use? 12. Brand X sells 21 oz. bags of mixed nuts that contain 29% peanuts. To make their product they combine Brand A mixed nuts which contain 35% peanuts and Brand B mixed nuts which contain 25% peanuts. How much of each do they need to use? 13. A 30% alcohol mixture is added to a 50% alcohol mixture to form a 10 liter mixture of 45% alcohol. How much of the 30% mixture was used? 14. Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4 times the amount of the second solution? kg of a mixture contains 30% sand and 70% clay. In order to make the mixture contain equal quantities of clay and sand, how much of the mixture is to be removed and replaced with pure sand? 16. Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk? lb of coffee P and 25 lb of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X? 3
4 1. Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of this mixture is X? A. 10%, B %, C. 40%, D. 50%, E % 2. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in onegallon or half gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture? A. 2, B. 2.5, C. 3, D. 3.5, E If 200 lb of a mixture contain 80% husk and 20% sand. Then how much husk needs to be extracted in order to have 75% concentration of Husk? A. 1/4, B. 20/3, C. 1/2, D. 40, E Rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture? A. 100, B. 140, C. 150, D. 160, E Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X? A. 30%, B. 33 1/3%, C. 37 1/2%, D. 40%, E. 50% 6. Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil? A. 15/29, B. 5/8, C. 5/16, D. 1/2, E. 13/27 7. A certain type of concrete mixture is to be made of cement, sand and graved in a ratio 1:3:5 by weight. What is the greatest number of kilograms of this mixture that can be made with 5 kilograms of cement? A. 13 1/2, B. 15, C. 25, D. 40, E Some of 50%intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced? A. 1/30, B. 1/5, C. 2/3, D. 3/4, E. 4/5 9. How many liters of pure alcohol must be added to a 100liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol? A. 7/2, B. 5, C. 20/3, D. 8, E. 39/4 10. One fourth of a solution that was 10 percent sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight? A. 34%, B. 24%, C. 22%, D. 18%, E. 8.5% 11. Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallon of 1 percent grade, y gallon of 2 percent grade, and z gallon of 3 percent grade are mixed to give x + y + z gallons of 1.5 percent grade, what is x in terms of y and z? A. y + 3z, B. y+z, C. 2y + 3z, D. 3y + z, E. 3y + 4.5z 4 4
5 12. A shade of paint is made by evenly mixing m gallons of white paint, costing $12 a gallon, with n gallons of blue paint, costing $30. What is the cost, in dollars per gallon, of the resulting mixture? A. 12m + 30n, B. 42(12m + 30n), C. 12m+30n, D. 12m+30n 42(M+N), E. 42 M+N 12m+30n 13. Some part of the 50% solution of acid was replaced with the equal amount of 30% solution of acid. As a result, 40% solution f acid was obtained. what part of the original solution was replaced? A. 1/5, B. 1/4, C. 1/2, D. 3/4, E. 4/5 14. A portion of the 85% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced? 15. According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12ounce cans of the concentrate are required to prepare ounce servings of orange juice? A. 25, B. 34, C. 50, D. 67, E There are two bars of goldsilver alloy; one piece has 2 part of gold to 3 parts of silver, and the other has 3 parts of gold to 7 parts of silver. If both bars are melted into an 8 kg bar with final ration of 5:11 of gold to silver, what was the weight of the first bar? A. 1 kg, B. 3 kg, C. 5 kg, D. 6 kg, E. 7 kg 17. Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance? A. 9/10, B. 1, C. 10/9, D. 20/19, E A mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture? A. 3/8, B. 8/15, C. 6/5, D. 5/3, E. 15/8 5
6 1. A cyclist travels at 12 miles per hour. How many minutes will it take him to travel 24 miles? (A) 1, (B) 2, (C) 30,(D) 60, (E) Point M is located 8 miles East of point P. If point P is located 6 miles North of another point A, then how far is point A from point M? (A) 4, (B) 5, (C) 6, (D) 7, (E) A wheat bag weighs 5 pounds and 12 ounces. How much does the bag weigh in pounds? (A) 5 1/4, (B) 5 1/2, (C) 5 3/4, (D) 6 1/4, (E) 6 3/4 4. One ton has 2000 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons? (A) 1600, (B) 1700, (C) 2350, (D) 2500, (E) An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 36 times the difference between the two numbers. How many coins did the old man have? (A) 24, (B) 26, (C) 30, (D) 36, (E) Patrick purchased 80 pencils and sold them at a loss equal to the selling price of 20 pencils. The cost of 80 pencils is how many times the selling price of 80 pencils? (A) 0.75, (B) 0.8, (C) 1, (D) 1.2, (E) A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 50 miles? (A) 300, (B) 318, (C) 322, (D) 324, (E) A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 6 members, then what is the exact number of researchers required? (A) 10, (B) 12, (C) 14, (D) 15, (E) The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers? (A) 20,000, (B) 22,000, (C) 25,000, (D) 30,000, (E) 40,000 (Next 2 questions) Mike and Fritz ran a 30mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles. Fritz ran the first onethird (by time) of the run at 10 miles per hour and the remaining twothirds of the run at 5 miles per hour. 10. How much time in hours did Mike take to complete the Marathon? (A) 3, (B) 3.5, (C) 4, (D) 4.5, (E) How much time in hours did Fritz take to complete the Marathon? (A) 3, (B) 3.5, (C) 4, (D) 4.5, (E) When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price? (A) 8, (B) 12, (C) 16, (D) 20, (E) 24 6
7 13. John has $42. He purchased fifty mangoes and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango? (A) 0.4, (B) 0.45, (C) 0.5, (D) 0.55, (E) In a market, a dozen eggs cost as much as a pound of rice, and a halfliter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? (A) 0.33, (B) 0.44, (C) 0.55, (D) 44, (E) Mr. Smith's average annual income in each of the years 1966 and 1967 is x dollars. His average annual income in each of the years 1968, 1969, and 1970 is y dollars. What is his average annual income in the five continuous years 1966 through 1970? (A) 2x 5 + 3y 5, (B) x 2 + y 2, (C) 5(x + y), (D) 5x 2 + 5y 2, (E) 3x 5 + 2y Hose A can fill a tank in 5 minutes, and Hose B can fill the same tank in 6 minutes. How many tanks would Hose B fill in the time Hose A fills 6 tanks? (A) 3, (B) 4, (C) 5, (D) 5.5, (E) How many coins of 0.5 dollars each and 0.7 dollars each together make exactly 4.6 dollars? (A) 1, 6, (B) 2, 7, (C) 3, 5, (D) 4, 3, (E) 5, A piece of string 35 inches long is cut into three smaller pieces along the length of the string. The length of the longest piece is three times the length of the shortest piece. Which one of the following could equal the length of the mediumsize piece? (A) 5, (B) 7, (C) 10, (D) 16, (E) Katrina has a wheat business. She purchases wheat from a local wholesaler at a particular cost per pound. The price of the wheat at her stores is $3 per pound. Her faulty spring balance reads 0.9 pounds for a pound. Also, in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Katrina purchase the wheat from the wholesaler? (A) 2.43, (B) 2.5, (C) 2.7, (D) 3, (E) A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph? (A) 65, (B) 50, (C) 45, (D) 40, (E) 35 7
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