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.

$73 per night

$24 per extra rollaway bed

Step-by-step explanation:

Let $x be the price per night in the hotel and $y be the cost for extra rollaway per night.

1st family:

The first family stayed for 5 nights and paid $5x for those 5 nights

Also they paid extra $2y for rollaway bed for 2 nights.

In total, they paid $(5x+2y) that is $413.

Hence,

2nd family:

The second family stayed for 3 nights and paid $3x for those 3 nights

Also they paid extra $y for rollaway bed for 1 night.

In total, they paid $(3x+y) that is $243.

Hence,

Solve the system of two equations:

Multiply the second equation by 2 and subtract it from the first equation:

Substitute it into the second equation:

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step-by-step explanation: