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A hotel has some rooms with two beds and some with one bed. The hotel charges 80 dollars a night for rooms with two beds and 60 dollars a night for rooms with one bed. The hotel has a total of 170 BEDS (that's 170 beds, not rooms). , and when the hotel is in full occupancy, they can make $7800 i one night, a. write down a system of equations with two variables to describe this situation. b. Solve this system to determine how many rooms have one bed and how many rooms have two beds.

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Nestor RutherfordLv2

14 Mar 2019

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This is a Project (Submit date: 2017/6/10)

Kindly Solve ALL The Project Requirments!

This Project is Related to and Part of "Linear Algabra and Differential Equations [Course]"

Systems of Linear Equations Project Introduction Systems of linear equations are a useful way to solve common problems in different areas of life. One of the most powerful ways to use them is in a comparison model where twosimilar situations are compared side by side todetermine which one is better. In this project, you will be choosin two real life situations and then using systems of linear equations to decide what to buy. The two situations are 1. Spending nights at a 3 star hotel in Paris, France or spending nights at a 5 star hotel in New York City. 2. Cell phone plans, comparing monthly fee and price per text message. You must use basic phones for the purpose of this project Cell Phone Plans Vacation Situation: You have graduated from high school Situation: You have graduated from high school and you are planning to go on a vacation by and moved away to college. Your parents have yourself. You have always wanted to travel to decided that it's time for you to pay for your Paris, France, but you need to consider the price own cell phone. You have to stick to a strict of the ticket as well as the costof hotel per budget. Now you need to determine whether you should go with a plan that costs more per night. As an alternative, you want to look into spending the same number of nights in Nev month but charges less per text message or a York City at a luxurious 5 star hotel. Now you cheaper plan that charges more per message need to determine whether you should go to Paris which will cost you for flight and hotel or nment: You are to choose from a cellphone stay in NYC that will cost you only for the hotel company that offers two talk and text plans. The company charges a monthly service fee of $20 Note: You are spending the same number of nights at each destination for either plan the customer chooses: Talk and Text Plan A charges five cents a Assignment: Gather information from travel minutes and twenty dollars for 250 texts Talk and Text Plan B charges ten cents a minute agencies, such as American Airline, Orbitz Expedia, or Kayak, through their website for cost (first 100 minutes free) and fifteen dollars for of flight and cost of hotel. Then write a system 200 texts of linear equations for the two plans and create NOTE: Assume you are purchasing a basic a graph. Use the methods we have been phone, which is $0 with 2-year contract. You studying to determine which plan is better cannot purchase unlimited text messaging for based on the number of nights you decide to this exercise. Use the methods we have been stay if you had$1500 to spend for this vacation studying to determine which plan is better based on the number of text messages you send per month if you only have S75 to spend each month Project Details You will decide which project you want to do. After you decide on a project, you wi need to 1) Collect the data if necessary. 2) write the system of linear equations and a word problem once the data has been collected 3) Use the methods we have been studying (graphing and solving algebraically) to find the solution to the written system. 4) Design the final display of the project on a poster board. Be creative

Show transcribed image text Systems of Linear Equations Project Introduction Systems of linear equations are a useful way to solve common problems in different areas of life. One of the most powerful ways to use them is in a comparison model where twosimilar situations are compared side by side todetermine which one is better. In this project, you will be choosin two real life situations and then using systems of linear equations to decide what to buy. The two situations are 1. Spending nights at a 3 star hotel in Paris, France or spending nights at a 5 star hotel in New York City. 2. Cell phone plans, comparing monthly fee and price per text message. You must use basic phones for the purpose of this project Cell Phone Plans Vacation Situation: You have graduated from high school Situation: You have graduated from high school and you are planning to go on a vacation by and moved away to college. Your parents have yourself. You have always wanted to travel to decided that it's time for you to pay for your Paris, France, but you need to consider the price own cell phone. You have to stick to a strict of the ticket as well as the costof hotel per budget. Now you need to determine whether you should go with a plan that costs more per night. As an alternative, you want to look into spending the same number of nights in Nev month but charges less per text message or a York City at a luxurious 5 star hotel. Now you cheaper plan that charges more per message need to determine whether you should go to Paris which will cost you for flight and hotel or nment: You are to choose from a cellphone stay in NYC that will cost you only for the hotel company that offers two talk and text plans. The company charges a monthly service fee of $20 Note: You are spending the same number of nights at each destination for either plan the customer chooses: Talk and Text Plan A charges five cents a Assignment: Gather information from travel minutes and twenty dollars for 250 texts Talk and Text Plan B charges ten cents a minute agencies, such as American Airline, Orbitz Expedia, or Kayak, through their website for cost (first 100 minutes free) and fifteen dollars for of flight and cost of hotel. Then write a system 200 texts of linear equations for the two plans and create NOTE: Assume you are purchasing a basic a graph. Use the methods we have been phone, which is $0 with 2-year contract. You studying to determine which plan is better cannot purchase unlimited text messaging for based on the number of nights you decide to this exercise. Use the methods we have been stay if you had$1500 to spend for this vacation studying to determine which plan is better based on the number of text messages you send per month if you only have S75 to spend each month Project Details You will decide which project you want to do. After you decide on a project, you wi need to 1) Collect the data if necessary. 2) write the system of linear equations and a word problem once the data has been collected 3) Use the methods we have been studying (graphing and solving algebraically) to find the solution to the written system. 4) Design the final display of the project on a poster board. Be creative

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Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x - y = 26 x - y = 170 and x + y = 26 2x + 170 - 26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 69 27 and 96 97 and 26 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72, 69) (27, 69) (72, 98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18,14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? Choose one answer. x + y = 100 and x + y = 36 x + y = 100 and 24x + 50y = 100 x + y = 100 and 24x + 50y = 36(100) x + y = 100 and 24 + 50 = 36

Show transcribed image text Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x - y = 26 x - y = 170 and x + y = 26 2x + 170 - 26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 69 27 and 96 97 and 26 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72, 69) (27, 69) (72, 98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18,14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? Choose one answer. x + y = 100 and x + y = 36 x + y = 100 and 24x + 50y = 100 x + y = 100 and 24x + 50y = 36(100) x + y = 100 and 24 + 50 = 36

Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x-y = 26 x-y = 170 and x + y = 26 2x + 170-26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 89 27 and 98 97 and 28 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72,89) (27,89) (72,98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18.14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? x + y = 100 and x + y = .36 x + y = 100 and .24x + .50y = 100 x + y = 100 and .24x + .50y = .36(100) x + y = 100 and .24 + .50 = .36

Show transcribed image text Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x-y = 26 x-y = 170 and x + y = 26 2x + 170-26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 89 27 and 98 97 and 28 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72,89) (27,89) (72,98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18.14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? x + y = 100 and x + y = .36 x + y = 100 and .24x + .50y = 100 x + y = 100 and .24x + .50y = .36(100) x + y = 100 and .24 + .50 = .36

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