Linear Algebra Word Problems

A dietitian is planning a meal that supplies certain quantities of vitamin C, calcium, and magnesium. Three foods will be used, their quantities measured in milligrams. The nutrients supplied by one unit of each food and the dietary requirements are given in the table below.
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The sum of three numbers is 26. Twice the first minus the second is 2 less than the third. The third is the second minus three times the first. Find the numbers.
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solve the matrix for x: 4= [x^2 xi ] [3xi x^2]
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A health club offers three different membership plans. With Plan A, you can use all club facilities: the pool, fitness center, and the racket club. With Plan B, you can use the pool and the fitness center. With Plan C,you can use the racket club. A single membership for Plan A is $420, Plan B is $360, and Plan C is $288. For a family membership, Plan A is $792, Plan B is $672, and Plan C is $528. Create a matrix that shows the cost for membership.
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Jane sells a driedfruit mixture for $5.80 per pound anh Hawaiian macadamian nuts for $14.75 per pound. She wants to blend the two to get a 15Lb mixture that she will sell for $9.38 per pound. How much of each should she use?
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A child`s piggy bank contains only nickels, dimes, and quarters. There are 75 coins in the bank, and the value of the coins is $7.25. If there are five times as many nickels as dimes, find the number of coins of each type in the bank.
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A passanger jet took three hours to fly 1800 miles in the direction of the jetstream. The return trip against the jetstream took four hours. What was the jet`s speed in the still air and the jetstreams speed?
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A delicatessen delivers a gigantic sandwich to be shared by 12 members of a jury who have been unable to reach a verdict. The sandwich consist of bread, meat, and cheese. The cost of the sandwich is $.60/lb for the bread, $3.00/lb for the meat, and $1.50/lb for the cheese. One pound of bread supplies 10g of protein, one pound of meat supplies 50g of protein, and one pound of cheee supplies 40g of protein. Each member of the jury pays $1.50 for a onepound portion of the sandwich. Each onepound portion contains 30g of protein. How much of each ingredient is in the whole sandwich?
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A food establishment with outlets in Soufriere and Castries sells three basic meals : grilled fish special, fried chicken special and jerked chicken special with prices of EC$28, EC$20 and EC$ 24 respectively. One weekend the outlet in Castries sold 60 grilled fish specials, 30 fried chicken specials and 45 jerk chicken specials . The outlet in Soufriere sold 40 grilled fish specials, 25 fried chicken specials and 30 jerk chicken specials on that same weekend. a. Is it possible for weekend sales to be displayed as a matrix/vector? If so, what is that matrix/vector and show its dimension. b. Is it possible for the unit prices of these meals to be displayed as a vector/matrix? If so, what is that vector/matrix and show its dimension. c. Is there anyway that the answers to a. and b. can be used to compute the total weekend sales for each outlet? If so, what is this way?
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Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 25 cents each, oatmean muffins at 40 cents each, and blueberry muffins at 35 cents each. Charles buys some muffins, including three times as many blueberry muffins as chocolate chip muffins. If he spends $6.50 on 20 muffins, how many oatmeal muffins did he buy?
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Stacy and theresa live 800 miles apart. Stacy`s speed is 4mph grgreater than theresa. They meet in 8 hours. WHaT aRE THEIR speeds>
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a lawn company has 3 kinds of fertilizer. Mix A contains 40% plant food and 40% weed killer. Mix B contains 60% plant food and 20% weed killer. Mix C contains 50% plant food and 24% weed killer. In mixing 2000 pounds of fertilizer, how many pounds of each mix must be used to have a mixture containing 52.5% plant food and 26% weed killer?
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a 5lb nut mixture is worth $2.80 per pound. The mixture contains peanuts worth $1.70 per pound and cashews worth $4.55 per pound. How many pounds of each type of nut are in the mixture?
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A small school has 100 students who occupy three classrooms: A, B, and C. Adter the first period of the school day, half the students in room A move to room B, one fifth of the students in room B move to room C, and onethird of the students in room C move to room A. Nevertheless, the total number of students in each room is the same for both periods. How many students occupy each room?
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A small fish market sells only tuna and salmon. A tuna costs the fish market $1.75 per pound to buy an $1.00 per pound to clean and package. A salmon cost the fish market $2.25 per pound to buy and $3.50 per pound to clean and package. The fish market makes $1.30 per pound profit for each tuna it sells and $1.60 per pound profit for each salmon it sells. The fish market can spend only $200 per day to buy fish and $225 per day to clean and package the fish. What is the maximum profit the fish owner can make per day and how much of each type of fish can he buy?
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A company`s employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work to receive full credit.
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The three American universities with the greatest endowments are Yale, Harvard, and Princeton. Their combined endowments total $12.09 bilion. Together, Yale and Princeton have $0.53 billion more in endowments than Harvard. Princeton`s endowments trail Harvard`s by $2.70 billion. What are the endowments for each of the universities?
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Big Red Bookstore wants to ship books from its warehouses in Brooklyn and Queens to its stores, one on Long Island and one in Manhattan. Its warehouse in Brooklyn has 1000 books, and its warehouse in Queens has 2000. Each store orders 1500 books. It costs $1 to ship each book from Brooklyn to Manhattan and $2 to ship each book from Queens to Manhattan. It costs $5 to ship each book from Brooklyn to Long Island and $4 to ship each book from Queens to Long Island. If Big Red has a transportation budget of $9000 and is willing to spend all of it, how many books should Big Red ship from each warehouse to each store in order to fill all the orders?
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A piggy bank is filled with quarters and dimes if thee value of the coins is $32.35 and there are 196 coins ,how many of the coins are dimes
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A company`s employees are working to create a energy bar. They would like two key ingredients to be chocolate and oats, and they want to make sure they have enough carbohydrates and protein and calcium in the bar to supply athletes. They want a total of 31 carbohydrates, 23 grams of protein, and 27 grams of calcium to make the bar sufficient.
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Five diabetic patients in a hospital each require injections of three kinds of insulin each day. The 5x3 matrix shown below gives the amounts of the three kinds of insulin each patient requires each day. If patient 1 plans to stay 10 days, patient 2 stays 5 days, patient 3 stays 20 days, patient 4 stays 10 days, and patient 5 stays 15 days, how much of each type of insulin must the medical staff have on hand?
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Two cups of coffee and three pieces of samosa cost $8, while one cup of coffee and 2 pieces of samosa cost $5. Find the cost of one cup of coffee and a piece of samosa
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midterm final system 1 system 2 student 1 73 79 midterm .3 ,5 student 2 44 62 Final .7 .5 student 3 76 88 student 4 98 96 What is the final course score for both grading systems
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The student council is selling hats and shirts for a fundraiser. Each hat sells for $12 and each shirt sells for $8. Hats and shirts will be sold at 3 different times during the day: before school, during lunch, and after school. One Monday before school, 7 hats and 10 shirts were sold. At lunch, 20 hats and 30 shirts were sold. After school, 10 hats and 20 shirts were sold.
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A fast food company sells three specials. The number of hamburgers, french fry orders, and sodas in each special is summarized below. The day`s reciept indicates that there were 300 hamburgers, 500 french fries, and 400 sodas sold. How many of each type of special were sold
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Colleen wants to purchase a $4000 used car, but only has $1000 available. Not wishing to finance the purchase, she makes a series of wagers in which the winnings equal whatever is bet. The probability of winning is .4 and the probability of losing is .6 In a daring strategy Colleen decides to bet all her money or at least enough to obtain $4000 until she loses everything or has $4000. That is, if she has $1000, she bets $1000; is she has $2000, she bets $2000; if she has $3000, she bets $1000.
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HaiLing is training for his piolet`s license. Flight instruction cosrs $105 per hour, and the simulator costs $45 per hour. The school requires students to spend 4 more hours in airplane training than in the simulator. If Hai_ling can afford $3870 on training, how many hours can he spend training in an airplane and in a simulator?
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Bethney`s animal shelter received a shipment of items worth $1040. NIck`s special blend of dog food is $5 a bag. Lisa`s handmade collars are $6 each and Cecilia`s pull toys are $2 each. There are 4 times as many bags of food as collars. The number of collars and toys totals 100. How many of each item are in the shipment?
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you want to have a pizza party this weekend for some friends and family. You have $48 budgeted for the pizza and plan on having 56 pieces available. A large pizza has 16 pieces and cost $14. A medium pizza has 12 pieces and cost $10.00. How many more large and medium pizzas do you need to buy?
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Joe has a total of 14 pennies, dimes and quaters in his pocket, which total $1.22. The number of dimes and quarters combined is equal to the number of pennies. How many of each coin does Joe have?
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Test 1 = 30% Test 2=30% Exam=40% Test 2=Test17grade points Exam=lowest test score 7 grade points Bio average=89% What are grades?
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Miguel`s coin collection consists of dimes and quarters. If he has 53 coins worth $7.85, how many of each type of coin does he have?
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a preschool has a Campbell\`s chunky beef soup, which contains 2.5 g of fat and 15 mg of cholesterol per cup, and Campbell\`s Chunky Sirloin burger soup, which contains 7g of fat, and 15 mg of cholesterol per serving. By combining the soups, it is possible to get 10 servings of soup that will have 61 g of fat, and 150 mg of cholesterol. How many cups of each soup should be used?
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A radiator in a large truck has a capacity of 10 gallons. Currently the radiator fluid is 20% antifreeze. How much fluid should be drained out and replaced with a 75% antifreeze solution to bring the solution in the radiator to 50% antifreeze? Set up and solve a system of equations to answer this question.
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kate borrows 10,000 some from her friend at 8% annual interest, twice as much as that from her ank at 9%, and the remainder from her insurance company at 5%. She pays a total of $ 830 interest for the first year. How much did she borrow from each source/
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kate borrows 10,000 some from her friend at 8% annual interest, twice as much as that from her ank at 9%, and the remainder from her insurance company at 5%. She pays a total of $ 830 interest for the first year. How much did she borrow from each source?
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a box contains nickels, dimes and pennies worth $8.40. The number of dimes is six less than twice the number of pennies and there is an equal number of dimes and nickels. How many nickels are there in the box?
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A chemist has 3 containers of acid solution at various concentrations. The first is 10% acid, the second is 20% and the third is 40%. How many milliliters of each should he mix together to make 100mL of acid at 18% concentration, if he has to use 4 times as much of 10% solution as the 40% solution?
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Two joggers are 2.0 mi apart. If they jog toward each other, they will meet in 12 minutes. If they jog in the same direction, the faster one will overtake the slower one in 2.0 hours. At what rate does each jog?
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A football stadium has 60,000 seats. The manager divides the stadium into two sections for the exhibition games, the games the home team plays outside its division, and the games it plays within its division. The tickets are worth $19 in section A and $14 in section B. Assuming that all tickets can be sold, how many seats must he assign to each section on says of an exhibition game, a game outside the division, and a game within the division to bring in the following revenues: $970,000 for each exhibition game, $990,000 for each game outside the division, and $1,120,000 for each game within the division.
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Steve catches 8 crocodiles on Sunday morning and 10 Sunday afternoon. On Wednesday morning, he catches 10 crocodiles in the morning and 9 crocodiles in the afternoon. What is the determinant?
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A survey of 900 college students found that 65% of the men and 90% of the women identified math as their favorite subject. If altogether 705 students reported math to be their favorite subject, how many men and women participated in the survey?
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Tasty Bakery sells three kinds of muffins: chocolate chip muffins at .30 cents each, oatmeal muffins at .35 cents each, and cranberry muffins at .40 cents each. Charles buys some of each kind and chooses twice as many cranberry muffins as chocolate chip muffins. If he spends $5.05 on 14 muffins, how many oatmeal muffins does he buy?
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The sum of three numbers is 4. The second number decreased by the third is equal to the first. The sum of the first and second number is 5. Find the numbers.
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Wendy`s sells singles and doubles. Toward the end of the evening, Wendy himself noticed that he had on hand only 32 patties and 34 slices of tomatoes. If a single takes 1 patty and 2 slices of tomato, and a double takes 2 patties and 1 slice of tomato, then how many singles and doubles can be made?
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Sonia Ramos is a chemist who is preparing an acid solution to be used as a cleaner for machine parts. The machine shop needs several 200mL batches of solution at a 48% concentration. Sonia only has 40% and 60% concentration solutions. The two solutions can be combined in some ratio to make the 48% solution. How much of each solution should Sonia use to make 200 mL of solution?
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A candy company packages caramels, chocolates, and hard candy in three differrent assortments: traditional, deluxe, and superb. For each type of candy the table below gives the number in each assortment, the number of calories per piece, and the cost to make each piece.

a preschool has a Campbell`s chunky beef soup, which contains 2.5 g of fat and 15 mg of cholesterol per cup, and Campbell`s Chunky Sirloin burger soup, which contains 7g of fat, and 15 mg of cholesterol per serving. By combining the soups, it is possible to get 10 servings of soup that will have 61 g of fat, and 150 mg of cholesterol. How many cups of each soup should be used?

Michael Perez has a total of $2000 deposited with two savings accounts. One pays interest at a 6% rate, whereas the second pays interest at the rate of 8%. If Michael earned a total of $144 in interest during a single year, how much does he have on deposit in each institution?

the mean time to run the maze was 138 seconds with a standard deviation of 18 seconds. What is the mean time in minutes? What is the standard deviation in minutes? What is the variance of time in minutes?

Calories can be burned during 20 min. of 3 different activities by people of different weights 120 lb person: bicycling (109), jogging (127), walking (64) 150 lb person: bicycling(136), jogging (159), walking (79) show how matrix multiplication can be used to write the total number of calories burned by a 120 lb person and a 150 lb person who each bicycled for 40 minutes, jog for 10 mkinutes, and walked for 60 minutes

6 rabbits and 5 cats cost 305 and 2 rabbits and 9 cats cost 285. How much does one cat cost?

Solve the following simultaneous equations using matrices: 2XY=3 X+5Y=7

I want to create a table for 20, 24,28 and 32 golfers , in groups of 4,on a 6 day tournament where no one plays with the same person twice.

To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Company produces 3 types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 7 hours for painting, 3 hours for drying, and 4 hours for polishing. A Beta requires 13 hours for painting, 6 hours for drying, and 5 hours for polishing. A Sigma requires 9 hours for painting, 2 hours for drying, and 3 hours for polishing. If the company has 254 hours for painting, 90 hours for drying, and 100 hours for polishing per month, how many of each type of car are produced.

A high school basketball coach helos the six seniors on the team to set goals for the season. The goals per game got each senior are as follows. Patrick: 2 3pointers, 10 field goals, 3 rebounds Mark: 1 3pointers, 6 field goals, 3 rebounds Joe: 3 3pointers, 5 field goals, 1 rebound Craig: 4 field goals, 6 rebounds Daryl: 4 field goals, 5 rebounds Mike: 3 field goals, 5 rebounds

HaiLing is training for his piolet\`s license. Flight instruction cosrs $105 per hour, and the simulator costs $45 per hour. The school requires students to spend 4 more hours in airplane training than in the simulator. If Hai_ling can afford $3870 on training, how many hours can he spend training in an airplane and in a simulator?

The sume of 3 number is 16. One of the numbers is the sum of the other two numbers. It is also four times the difference between the others two numbers. What are the three numbers?

Nick goes to the amusement park to ride roller coasters, bumper cars, and water slides. The wait for the roller coasters is 1 hour, the wait for the bumper cars is 20 minutes long, and the wait for the water slides is only 15 minutes long. Nick rode 10 total rides during his visit. Because he enjoys roller coasters most, the number of times he rose roller coasters was the sum of the time he rode the other two rides. If Nick waited in line for a total of 6 hours and 20 minutes, how many of each ride did he go on?

Miguel\`s coin collection consists of dimes and quarters. If he has 53 coins worth $7.85, how many of each type of coin does he have?

a $4 each. $90 worth of shirts were sold. how manywhite shirts were sold?

A bank lent 1.2 million for the development of three new products, with one loan each at 6%,7%, and 8%. The amount lent at 8% was equal to the sum of the amounts lent at the other two rates, and the bank`s annual income from the loans was s88,000. How much was lent at each rate?

Cabrina and Dabney are attending a conference. After the conference. Cabrina drives home to Boise at an average speed of 75 miles per hour and Dabney drives hom to Portland at an average speed of 60 miles per hour. If the sum of their driving times is 11.6 hours and if the sum of the distance drives is 801 miles, determine the time each woman spent driving home.

A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.

A hotel chain has three different hotels in Paris. The revenue (in thousands of dollars) from room rentals for one week in each hotel is $125, $600 and $340. Write a row matrix summarizing the revenue from room rentals.

Poulson Law Firm handles 2 types of law suits: medical malpractice suits and wrongful termination suits. Malpractice lawsuits each require 6 months of preparation and the hiring of 5 expert witnesses, whereas termination lawsuits require 10 months of preparation and 3 expert witnesses. The firm has a total of 30 months to work with and feels that it cannot afford to hire more than 15 expert witnesses. It makes an average profit of $10,000 per doctor sued and $50,000 per employer sued. How many of each type of lawsuit should it initiate in order to maximize profit?