Advanced Algebra: Linear Algebra Word Problems
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Advanced Algebra: Linear Algebra WordProblems
A company`s employees are working
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.
| Carbohydrates | Protein |
| Peanut Butter | 2 | 6 |
| Oats | 5 | 1 |
Steve catches 8 crocodiles
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 ...
A football stadium has 60,000 seats
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...
A chemist has 3 containers of acid solution
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% ...
A small fish market sells only tuna and salmon
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 ...
A survey of 900 college students
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 ...
The three American universities with the greatest endowments
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 ...
cramers rule
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 ...
Poulson Law Firm handles 2 types of law suits
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 ...
A small school has 100 students
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 ...
A group of students decides to sell pizzas
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 ...
