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
∵ The first family paid extra to use a roll away bed for 1 of the night
∵ The cost of the roll away bed per night is $b
∴ The cost of the two nights = b
∵ Their total bill was $243
∴ 3h + b = 243 ⇒ (2)
The system of equations that can be used is
5h + 2b = 413
3h + b = 243
Bart B:
∵ 5h + 2b = 413 ⇒ (1)
∵ 3h + b = 243 ⇒ (2)
- Multiply equation (2) by -2 to eliminate b
∴ -6h - 2b = -486 ⇒ (3)
- Add equations (1) and (3)
∴ -h = -73
- Multiply both sides by -1
∴ h = 73
Substitute the value of h in equations (1) or (2) to find b
∵ 3(73) + b = 243
∴ 219 + b = 243
- Subtract 219 from both sides
∴ b = 24
The cost per night of renting a room is $73 and the cost per night using a roll away bed is $24
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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