A food server examines the amount of money earned in tips after working an 8-hour shift. The server has a total of $191 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 53. Thenumber of $5 bills is 4 times the number of $10 bills, and the number of $1 bills is 1 less than twice the number of $5 bills. Write a system of linear equations to represent the situation. (Assumex = number of $1 bills, y = number of $5 bills, z = number of $10 bills, and w = number of $20 bills.)X +у +z +w = 191X +y +z +53W3=y --1Use matrices to find the number of each denomination.X =$1 bill(s)y =$5 bill(s)z =$10 bill(s)w =$20 bill(s)

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Answered: A food server examines the amount of…

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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$5000 is invested into two accounts. One pays 5% interest and the other pays 7%. The total investment earned $310 interest. Write the system of equations that describes this situation and then solve the system to determine how much was invested at 5% interest and how much was invested at 7% interest. Submit your system, solution steps, and final answer.
A food server examines the amount of money earned in tips after working an 8-hour shift. The server has a total of $133 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 39. The number of $5 bills is 4 times the number of $10 bills, and the number of $1 bills is 1 less than twice the number of $5 bills. Write a system of linear equations to represent the situation. (Assume x = number of $1 bills, y = number of $5 bills, z = number of $10 bills, and w = number of $20 bills.) X + y + z + W = 133 X + y + z + W = 39 у — X - y -1 Use matrices to find the number of each denomination. $1 bill(s) $5 bill(s) X = y = z = $10 bill(s) w = $20 bill(s)
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.
A health food company wishes to make a trail mix consisting of dried fruit (costing $4 per pound) and mixed nuts (costing $8 per pound) for a total cost of $900. A total of 150 pounds of trail mix should be made, with there being twice as much dried fruit as mixed nuts. Set up a system of equations that models the problem. Identify all variables.
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
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…
At a school cafeteria a cold lunch costs $1.80, and a hot lunch costs $3.00. During one school year a teacher spent a total of $288.60 on cold lunches and hot Ilunches. The number of cold lunches the teacher bought was 1 fewer than twice the number of hot lunches the teacher bought. Which system of equations can be used to find the number of cold lunches, and h, the number of hot lunches, the teacher bought during the school year? 3.00c + 1.80h = 288.60 h = 1- 2c 1.80c + 3.00h = 288.60 C = 1- 2h 3.00c + 1.80h = 288.60 1-18 10 11 12 13 > Back Review/End Next 1 5 6 7 9 us O I1
An apartment complex has 1-bedroom apartments and 2-bedroom apartments. There are a total of 78 apartments in the complex, and there are twice as many 2-bedroom apartments as 1-bedroom apartments. If you want to find the number of apartments of each type, which system of equations could be used to solve the problem? Let x be the number of 1-bedroom apartments, and let y be the number of 2-bedroom apartments. A. x + y = 78 2 + y = x B. x + y = 78 2x = y C. x + y = 78 2y = x D. x + 2y = 78 2y = x E. x + 2y = 78 2x = y

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