Mixture Problems set 1

Transcription

1 Mixture Problems set 1 1. A mixture contains 7 ounces of turpentine and 28 ounces of water. a. What is the fraction of turpentine in the mixture? the percent? b. What is the fraction of water in the mixture? the percent? c. If 7 ounces of water is added to the original mixture, what is the fraction of turpentine in the new mixture: the percent? d. If 7 ounces of turpentine is added to the original mixture what is the fraction of turpentine in the new mixture? the percent? 2. In a mixture of 50 ounces of borax and water there is 10% borax. a. How much borax is in the mixture? how much water? b. What fraction of borax is in the mixture? What fraction of water? c. 10 ounces of borax is added to the mixture. What is the total amount of borax in the new mixture? What is the total amount of the new mixture? What is the fraction of borax in the new mixture? d. 5 ounces of water is added to the original mixture. How much borax is in the new mixture? What is the total of new mixture? What is the fraction of borax in the new mixture? What is the percent? 3. Solution A is 50% acid and solution B is 80% acid. How much of each should be used to make 100 cc. of a solution that is 68% acid? 4. Solution A is 30% alcohol and solution B is 75% alcohol. How much of each should be used to make 100 liters of a solution that is 50% alcohol? 5. A candy mix sells for $2.20 per kilogram. It contains chocolates worth $1.80 per kilogram and other candy worth $3.00 per kilogram. How much of each are in 15 kilograms of the mixture? 6. The "Nuthouse" has 10 kg. of mixed cashews and pecans worth $4.80 per kg. Cashews alone sell for $3.00 per kg. and pecans sell for $6.00 per kg. How many kilograms of each are in the mixture? 7. To make a weed and feed mixture, the Green Thumb Garden Shop mixes fertilizer worth $4.00/lb. with a weed killer worth $8.00/lb. The mixture will cost $6.00/lb. How much of each should be used to prepare 500 lb. of the mixture? 8. Farmer Jones has 100 liters of milk that is 4.6% butterfat. How much skim milk (no butterfat) should be mixed with it to make milk that is 3.2% butterfat? 9. A tank contains 8000 liters of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid? 10. A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 qt. of a solution containing 42% insecticide. How much of each solution is to be used? Mixture Problems 1

2 11. A grocer is mixing 40 cent per lb. coffee with 60 cent per lb. coffee to make a mixture worth 54 cents per lb. How much of each kind of coffee should be used to make 70 lb. of the mixture? 12. One morning farmer Brown's wife found the dogs in the barnyard chasing the chickens. She counted 40 heads and 86 feet total. How many dogs and how many chickens were there? 13. How much antifreeze should be added to 5 quarts of a 30% mixture of antifreeze to make a solution that is 50% antifreeze? 14. A car radiator holds 10 quarts of liquid. If the liquid in the radiator is 30% antifreeze, how much of the liquid must be replaced with pure antifreeze to bring the solution up to the recommend 50% antifreeze? 15. Three quarts of gasoline are mixed with 5 quarts of kerosene; how many quarts of kerosene must be added to make the mixture 3 4 kerosene? 16. In a mixture of water and turpentine containing 21 ounces, there are 7 ounces of turpentine. How many ounces of turpentine must be added to make a new mixture which is 3 4 turpentine? 17. A mixture contains 4 pints alcohol and 6 pints water. How many pints of water must be added in order that the resulting mixture shall be 5% alcohol? 18. How much water must be added to a gallon of alcohol which is 90% pure alcohol to reduce it to 80% pure alcohol? 19. Of 12 pounds of salt water 10% is salt; of another mixture 3% is salt. How many pounds of the second should be added to the first in order to get a mixture 5% salt? 20. An automobile radiator has a capacity of 4 gallons. It is filled with a mixture of water and alcohol of which 10% is alcohol. How much of the mixture must be drawn off and replaced by alcohol to have the radiator contain a mixture that is 25% alcohol? 21. How much alcohol must be added to 24 gallons of a 14% solution of alcohol in order to produce a 20% solution? 22. How many gallons of an 85% solution of salt and a 70% solution of salt must be taken so as to form a mixture of 90 gallons which shall be % pure? 23. How many pounds of a 4% solution of borax must be added to 24 pounds of a 12% solution of borax to obtain a 10% solution of borax? Mixture Problems 2

3 24. A certain grade of milk contains 10% butter fat and a certain grade of cream 60% butter fat. How many quarts of each must be taken so as to obtain a mixture of 100 quarts that will be 45% butter fat? 25. A bottle contains 80 gallons of acid which is 25% pure acid. How much water must be drawn off from the acid to make it a 50% solution? 26. A merchant has tea worth 65 cents per pound and also tea worth 50 cents per pound; how many pounds of each must he use to make a mixture 12 pounds worth 60 cents per pound? 27. A grocer wishes to mix sugar at 9 cents per pound with sugar at 6 cents per pound to make 60 pounds at 7 cents per pound. What quantity of each must he take? 28. A grocer has two grades of tea, a 50 cent grade and a 70 cent grade. He wishes to make a mixture which he can sell for 55 cents per pound. How many pounds must he use in a mixture of 120 pounds? 29. A farmer has some cream which is 21% butterfat and some which is 15% butterfat. How many gallons of each must be mixed to produce 60 gallons of cream which is 19% butterfat? 30. A chemist has some 8% hydrogen peroxide solution and some 5% hydrogen peroxide solution. How many milliliters of each should be mixed to make a 300 milliliter solution which is 6% hydrogen peroxide? 31. How many grams of pure acid must be added to 40 grams of a 20% acid solution to make a solution which is 36% acid? 32. How many ounces of pure water must be added to 60 ounces of a 15% salt solution to make a salt solution which is 10% salt? 33. A hygienist mixed 50 L of a 36% disinfectant solution with a 40 L of water. What is the percent concentration of the resulting solution? 34. A researcher mixed 80 lb. of a 30% aluminum alloy with 120 lb. of a 25% aluminum alloy. What is the percent concentration of the resulting alloy? 35. A syrup manufacturer has some pure maple syrup and some which is 85% maple syrup. How many liters of each should be mixed to make 150 L which is 96% maple syrup? 36. A butcher has some hamburger which is 20% fat and some which is 15% fat. How many pounds of each should be mixed to make 50 pounds of hamburger which is 18% fat? Mixture Problems 3

4 37. A 100 LB bag of animal feed is 40% oats. How many pounds of oats must be added to this feed to produce a mixture which is 50% oats? 38. A goldsmith has 10 grams of a 50% gold alloy. How many grams of pure gold should be added to the alloy to make an alloy which is 75% gold? 39. Ten grams of sugar are added to a 40 gram serving of a breakfast cereal which is 30% sugar. What is the percent concentration of sugar in the resulting mixture? 40. Thirty ounces of pure grapefruit juice is added to 50 ounces of a fruit punch which is 20% grapefruit juice. What is the percent concentration of grapefruit juice in the resulting mixture? 41. You are taking a test in which items of type A are worth 10 points and items of type B are worth 15 points. It takes 3 minutes for each type A item and 6 minutes for each type B item. The total time allowed is 60 minutes and you can do exactly 16 questions. If you need to make a score of 180 points, how many questions of each type should you answer in the 60 minutes? 42. The goldsmith has two alloys that are different purities of gold. The first is 3 pure 4 gold and the second is 5 pure gold. How many ounces of each should be melted 12 and mixed to obtain a 6 ounce alloy that is 2 gold? A merchant has two kinds of paint. If 9 gallons of the inexpensive paint is mixed with 7 gallons of the expensive paint, the mixture will be worth $19.70 per gallon. If 3 gallons of the inexpensive paint is mixed with 5 gallons of the expensive paint, the mixture will be worth $ per gallon. What is the price per gallon of each type of paint? 44. A printer knows that a page of print contains 1300 words if large type is used and 1850 words if small type is used. A document containing 18,526 words fills exactly 12 pages. How many pages are in the large type and how many are in the small type? 45. A total of $27,000 is invested, part of it at 12% and the remainder at 13%. The total interest after one year is $3385. How much was invested at each rate? 46. A student earned $288 on investments. If $1100 was invested at one yearly rate and $1800 at a rate that was 1.5% higher, find the two rates of interest. 47. An automobile radiator contains 16 liters of antifreeze and water. This mixture is 30% antifreeze. How much of the mixture should be drained and replaced with pure antifreeze so that the mixture will be 50% antifreeze? Mixture Problems 4

5 48. An employer has a daily payroll of $325 when employing some workers at $20 per day and others at $25 per day. When the number of $20 workers is increased by 50% and the number of $25 workers is decreased by 1, the new daily payroll is 5 $400. How many workers were originally employed at each rate? 49. In Lewis Carroll's "Through the Looking Glass," Twedledum says to Tweedledee, "The sum of your weight and twice mine is 361 pounds." Then Tweedledee says to Tweedledum, "Contrariwise, the sum of your weight and twice mine is 362 pounds." Find the weight of Tweedledum and Tweedledee. set 2 1. A high-protein diet supplement that costs $6.75 per pound is mixed with a vitamin supplement that costs $3.25 per pound. How many pounds of each should be used to make 5 lb of a mixture that costs $4.65 per pound? 2. A 20 oz alloy of platinum that costs $220 per ounce is mixed with an alloy that costs $400 per ounce. How many ounces of the $400 alloy should be used to make an alloy that costs $300 per ounce? 3. Find the cost per pound of a coffee mixture made from 8 lb of coffee that costs $9.20 per pound and 12 lb of coffee that costs $5.50 per pound. 4. How many pounds of tea that cost $4.20 per pound must be mixed with 12 lb of tea that cost $2.25 per pound to make a mixture that costs $3.40 per pound? 5. A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.50 per ounce? 6. How many liters of a solvent that costs $80 per liter must be mixed with 6 L of a solvent that costs $25 per liter to make a solvent that costs $36 per liter? 7. Find the cost per pound of a trail mix made from 40 lb of raisins that cost $4.40 per pound and 100 lb of granola that cost $2.30 per pound. 8. Find the cost per ounce of a mixture of 200 oz of a cologne that costs $5.50 per ounce and 500 oz of a cologne that costs $2.00 per ounce. 9. How many kilograms of hard candy that cost $7.50 per kilogram must be mixed with 24 kg of jelly beans that cost $3.25 per kilogram to make a mixture that sells for $4.50 per kilogram? 10. A grocery store offers a cheese and fruit sampler that combines cheddar cheese that costs $8 per kilogram with kiwis that cost $3 per kilogram. How many kilograms of each were used to make a 5 kg mixture that costs $4.50 per kilogram? Mixture Problems 5

6 11. A ground meat mixture is formed by combining meat that costs $2.20 per pound with meat that costs $4.20 per pound. How many pounds of each were used to make a 50 lb mixture that costs $3.00 per pound? 12. A lumber company combined oak wood chips that cost $3.10 per pound with pine wood chips that cost $2.50 per pound. How many pounds of each were used to make an 80 lb mixture costing $2.65 per pound? 13. How many kilograms of soil supplement that costs $7.00 per kilogram must be mixed with 20 kg of aluminum nitrate that costs $3.50 per kilogram to make a fertilizer that costs $4.50 per kilogram? 14. A caterer made an ice cream punch by combining fruit juice that costs $2.25 per gallon with ice cream that costs $3.25 per gallon. How many gallons of each were used to make 100 gal of punch costing $2.50 per gallon? 15. The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100 lb mixture that cost $3.24 per pound? 16. Find the cost per gallon of a carbonated fruit drink made from 12 gal of fruit juice that costs $4.00 per gallon and 30 gal of carbonated water that costs $2.25 per gallon. 17. Find the cost per pound of a sugar-coated breakfast cereal made from 40 lb of sugar that costs $1.00 per pound and 120 lb of corn flakes that cost 60c/ per pound. 18. Find the cost per ounce of a gold alloy made from 25 oz of pure gold that costs $482 per ounce and 40 oz of an alloy that costs $300 per ounce. 19. How many pounds of lima beans that cost 90c/per pound must be mixed with 16 lb of corn that costs 50c/ per pound to make a mixture of vegetables that costs 65c/ per pound? 20. How many liters of a blue dye that costs $1.60 per liter must be mixed with 18 L of anil that costs $2.50 per liter to make a mixture that costs $1.90 per liter? 21. A chemist wants to make 50 ml of a 16% acid solution by mixing a 13% acid solution and an 18% acid solution. How many milliliters of each solution should the chemist use? 22. How many pounds of coffee that is 40% java beans must be mixed with 80 lb of coffee that is 30% java beans to make a coffee blend that is 32% java beans? 23. Thirty ounces of pure silver are added to 50 oz of a silver alloy that is 20% silver. What is the percent concentration of silver in the resulting alloy? Mixture Problems 6

7 24. Two hundred liters of punch that contains 35% fruit juice is mixed with 300 L of a second punch. The resulting fruit punch is 20% fruit juice. Find the percent concentration of fruit juice in the second punch. 25. The manager of a garden shop mixes grass seed that is 60% rye grass with 70 lb of grass seed that is 80% rye grass to make a mixture that is 74% rye grass. How much of the 60% mixture is used? 26. 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? 27. A dermatologist mixes 50 g of a cream that is 0.5% hydrocortisone with 150 g of a second hydrocortisone cream. The resulting mixture is 0.68% hydrocortisone. Find the percent concentration of hydrocortisone in the second hydrocortisone cream. 28. A carpet manufacturer blends two fibers, one 20% wool and the second 50% wool. How many pounds of each fiber should be woven together to produce 600 lb of a fabric that is 28% wool? 29. A hair dye is made by blending a 7% hydrogen peroxide solution and a 4% hydrogen peroxide solution. How many milliliters of each are used to make a 300 ml solution that is 5% hydrogen peroxide? 30. How many grams of pure salt must be added to 40 g of a 20% salt solution to make a solution that is 36% salt? 31. How many ounces of pure water must be added to 50 oz of a 15% saline solution to make a saline solution that is 10% salt? 32. A paint that contains 21% green dye is mixed with a paint that contains 15% green dye. How many gallons of each must be used to make 60 gal of paint that is 19% green dye? 33. A goldsmith mixes 8 oz of a 30% alloy with 12 oz of a 25% gold alloy. What is the percent concentration of the resulting alloy? 34. A physicist mixes 40 L of liquid oxygen with 50 L of liquid air that is 64% oxygen. What is the percent concentration of oxygen in the resulting mixture? 35. How many ounces of pure bran flakes must be added to 50 oz of cereal that is 40% bran flakes to produce a mixture that is 50% bran flakes? 36. How many milliliters of pure chocolate must be added to 150 ml of chocolate topping that is 50% chocolate to make a topping that is 75% chocolate? 37. A tea that is 20% jasmine is blended with a tea that is 15% jasmine. How many pounds of each tea are used to make 5 lb of tea that is 18% jasmine? Mixture Problems 7

8 38. A clothing manufacturer has some pure silk thread and some thread that is 85% silk. How many kilograms of each must be woven together to make 75 kg of cloth that is 96% silk? 39. How many ounces of dried apricots must be added to 18 oz of a snack mix that contains 20% dried apricots to make a mixture that is 25% dried apricots? 40. A recipe for a rice dish calls for 12 oz of a rice mixture that is 20% wild rice and 8 oz of pure wild rice. What is the percent concentration of wild rice in the 20 oz mixture? 41. Find the cost per ounce of a mixture of 30 oz of an alloy that costs $4.50 per ounce, 40 oz of an alloy that costs $3.50 per ounce, and 30 oz of an alloy that costs $3.00 per ounce. 42. A grocer combined walnuts that cost $1.60 per pound and cashews that cost $2.50 per pound with 20 lb of peanuts that cost $1.00 per pound. Find the amount of walnuts and the amount of cashews used to make the 50 lb mixture costing $1.72 per pound. 43. How many ounces of water evaporated from 50 oz of a 12% salt solution to produce a 15% salt solution? 44. A chemist mixed pure acid with water to make 10 L of a 30% acid solution. How much pure acid and how much water did the chemist use? 45. How many grams of pure water must be added to 50 g of pure acid to make a solution that is 40% acid? 46. A radiator contains 15 gal of a 20% antifreeze solution. How many gallons must be drained from the radiator and replaced by pure antifreeze so that the radiator will contain 15 gal of a 40% antifreeze solution? Mixture Problems 8

9 Answers set , choc, 5 other each @40, 49@ chickens, 3 dogs milk, 70 cream & @21%, 20@15% gram % @85%, 110 pure lbs % A, 4B 43. $19.408, $ ,500@12%, set diet, 3 vitamin $ lb of $4.30, 144 of $ $ $ cheese, 3.5 kiwis of $2.20, 20 of $ oak, 60 pine fruit, 25 ice almonds, 63 walnuts 16. $ c/ 18. $ of 13%, 30 of 18% % % % % of 20%, 160 of 50% of 7%, 200 of 4% of 21%, 20 of 15% % % of 20%, 2 of 15% of pure, 20 of 85% % 41. $ walnuts, 20 cashews pure acid, 7 water Mixture Problems 9