Answer:
$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, [tex]5x+2y=413[/tex]
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, [tex]3x+y=243[/tex]
Solve the system of two equations:
[tex]\left\{\begin{array}{l}5x+2y=413\\ \\3x+y=243\end{array}\right.[/tex]
Multiply the second equation by 2 and subtract it from the first equation:
[tex]5x+2y-(6x+27)=413-2\cdot 243\\ \\5x+2y-6x-2y=413-486\\ \\-x=-73\\ \\x=73[/tex]
Substitute it into the second equation:
[tex]3\cdot 73+y=243\\ \\219+y=243\\ \\y=243-219\\ \\y=24[/tex]
