Question

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.

Answer 1

$73 per night

$24 per extra rollaway bed

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,
`5x+2y=413`

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,
`3x+y=243`

Solve the system of two equations:

`\left\{\begin{array}{l}5x+2y=413\\ \\3x+y=243\end{array}\right.`

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

`5x+2y-(6x+27)=413-2\cdot 243\\ \\5x+2y-6x-2y=413-486\\ \\-x=-73\\ \\x=73`

Substitute it into the second equation:

`3\cdot 73+y=243\\ \\219+y=243\\ \\y=243-219\\ \\y=24`