Two families stayed at the same hotel in identical rooms. The first family stayed for 5 nights and paid extra to use a rollaway

Question

3 years ago

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Two families stayed at the same hotel in identical rooms. The first family stayed for 5 nights and paid extra to use a rollaway

bed for 2 of the nights. Their total bill was $413. The second family stayed for 3 nights and used a rollaway bed for 1 night. Their total bill was $243.
Part A
Write a system of equations that can be used to find, h, the cost per night of renting a room at the hotel, and b, the cost per night of using a rollaway bed at the hotel.

Part B
Use the elimination method to solve the system of equations from Part A for h and b. Show your work and explain the steps you take.

Mathematics

1 answer:

Vesna [10] · Answer 1 · 2022-06-24T03:02:58+03:00

Part A: The system of equations that can be used is

5h + 2b = 413

3h + b = 243

Part B: The cost per night of renting a room is $73 and the cost per night using a roll away bed is $24

Step-by-step explanation:

Two families stayed at the same hotel in identical rooms

The first family stayed for 5 nights and paid extra to use a roll away bed for 2 of the nights.
Their total bill was $413
The second family stayed for 3 nights and used a roll away bed for 1 night.
Their total bill was $243

We need to write a system of equations that can be used to find, h, the cost per night of renting a room at the hotel, and b, the cost per night of using a roll away bed at the hotel and find the values of h and b using the elimination method

Part A:

∵ The first family stayed for 5 nights

∵ The cost of the renting room per night is $h

∴ The cost of the five nights = 5h

∵ The first family paid extra to use a roll away bed for 2 of the nights

∵ The cost of the roll away bed per night is $b

∴ The cost of the two nights = 2b

∵ Their total bill was $413

∴ 5h + 2b = 413 ⇒ (1)

∵ The second family stayed for 3 nights

∵ The cost of the renting room per night is $h

∴ The cost of the five nights = 3h