10. Raul has an uncle who likes to play games when he visits. On his most recent visit, he told Raul that hecould have all the money in his wallet if he were able to guess how many of each kind of bill be had. Hereare the clues he gave:I have only 3 denominations of bills - $5 bills, $10 bills and $20 bills.●I have a total of 17 bills in my wallet.●The value of all the money in my wallet is $180.●I have twice as many $5 bills as I do $10 bills.Write a system of 3 linear equations to represent this situation and then use matrices to solve for x, thenumber of $5 bills, y, the number of $10 bills and z, the number of $20 bills in his wallet.

Answered: Image /qna-images/answer/309ffeb2-d2cf-4173-8fdd-07fce94eef84.jpg

Answered: could have all the money in his wallet…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Kelly has $24,500 to invest. She decides to divide it into the three accounts listed. At the end of the year, she has earned $1,300 in interest. If the amount invested in Stewart Oil was four times the amount of money invested in Thomas Games, how much did Kelly invest in each account? a. Write down the system of equations describing this situation. Be sure to define the variables. Company Yield Stewart Oil 4% Thomas Games 5.5% Kaitlyn Fragrances 6% State the matrix for this system of equations. Write down the reduced-row echelon form (i.e., the “answer matrix”) given by your calculator. Explain in 1-2 sentences the meaning of these results.
A golf resort offers two getaway options. The Mini Escape includes 2 nights' stay and 2 rounds of golf, and the Grand Escape includes 3 nights' stay and 4 rounds of golf. The Mini Escape costs $376 and the Grand Escape costs $619. Use a system of equations to find the cost for a one night's stay and the cost for one round of golf for these options.
The admission fee at an amusement park is $10.75 for children, $16 for adults, and $15 for seniors. On Monday, 6806 people entered the park, and the admission fees collected totaled $87332. Typically on any given day, the number of seniors who enter the park is about 500 less than the number of adults who come. On Monday, how many children, seniors, and adults were admitted? Write a system of equations; solve using your calculator and the matrix key. Answer: There were children, adults, and seniors.
Translate to a system of equations and solve. Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $7.80 per pound with French Roast Columbian coffee that cost $8.10 per pound to make a 20 pound blend. Their blend should cost them $7.92 per pound. How many pounds of each type of coffee should they buy? City Roast Columbian French Roast Columbian
Three friends went to the fair. Michelle ate three hot dogs, one pretzel, and two snow cones. She spent $25. Amanda ate two hot dogs, three pretzels, and three snow cones. She spent $30. Lucas ate two hot dogs, two pretzels, and four snow cones. He spent $25. Which system of equations matches the friends' night at the fair? Answer 1 2x + y + 3z = 252x + 3y + 3z = 302x + 2y + 4z = 25 Answer 2 3x + y + 2z = 252x + 3y + 3z = 302x + 2y + 4z = 25 Answer 3 3x + y + 2z = 253x + 2y + 3z = 302x + 2y + 4z = 25 Answer 3x + y + 2z = 252x + 3y + 3z = 302x + 4y + 2z = 25
The Chess Club ordered 10 pizzas and 5 dozen chicken wings, which came to a total of $100. At the same time, the Spanish Club ordered 12 pizzas and 4 dozen chicken wings for a total of $108. Let x = the cost of a pizza and y = the cost of a dozen chicken wings. Write a system of equations that would enable you to solve how much each item costs. DO NOT solve for the prices. Just write the system of equations.
Write a system of 3 equations in 3 unknowns for this problem. You must label your variables. Do NOT solve the system! A store sells tents, sleeping bags, and lanterns. A customer buys a tent, 7 sleeping bags, and 3 lanterns for $156. The price of the tent is 5 times the cost of a lantern. The cost of a sleeping bag is $3 more than the cost of a lantern. Write a system of equations to find the cost of each item. geph X= y%3D 15) (ral gulip
Two teachers, Mrs. Dewsbury and Mrs. Pettit, decide to buy calculators and stickers for their classrooms. Mrs. Dewsbury buys 30 calculators and 50 pages of stickers for $95. Mrs. Pettit buys 40 calculators and 40 pages of stickers of each for $116. Write a system of equations to represent the cost of one calculator, c, and one page of stickers, p. A. c + p = 120 70c + 90p = 211 B. c + p = 211 30c + 50p = 40c + 40p C. 30c + 50p = 95 40cp = 116 D. 30c + 50p = 95 40c + 40p = 116
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Nanh is really into magic tricks and decides to put on a show to buy more magic trick kits and accessories. She sells three types of tickets to the show. Adult tickets are $10, young adult tickets are $8, and child tickets are $4. Nanh sells a total of 21 tickets and brings in $140. The number of child tickets sold is twice the number of young adult tickets sold. Write a system of equations to represent this situation where x is the number of adult tickets sold, y is the number of young adult tickets sold, and z is the number of child tickets sold. How many of each type of ticket did Nanh sell? With the $140 she made from the magic show, Nanh now needs to decide what magic tricks she wants to purchase. Small magic kits cost $3 each and larger kits cost $7 each. Nahn wants to buy at least 28 magic kits. Write a system of inequalities to model this situation letting x = the number of small magic kits and y = the number of large magic kits. Then graph the system of inequalities…
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