To find the correct linear equation that represents how much Martina collects for one night of stay in her home, let's break down the charges clearly:
1. Flat Fee for One Person: Martina charges a flat fee of [tex]$25 per night for one person.
2. Additional Guests: For each additional guest, Martina charges an extra $[/tex]10. Let [tex]\( p \)[/tex] represent the number of additional guests.
3. Late Checkout Fee: Martina charges an extra [tex]$5 per hour for late checkouts. Let \( h \) represent the number of late checkout hours.
Now, let's combine these charges into a linear equation to represent the total cost \( c \):
- The base charge for the room is $[/tex]25.
- Each additional guest increases the cost by [tex]$10, so the cost due to additional guests is \( 10p \).
- Each late checkout hour increases the cost by $[/tex]5, so the cost due to late checkout is [tex]\( 5h \)[/tex].
To form the equation that gives the total charge [tex]\( c \)[/tex]:
[tex]\[ c = 25 + 10p + 5h \][/tex]
Given the options, we see that:
A) [tex]\( c = 25 + 10 + 5 \)[/tex] does not incorporate variables for the number of guests or late checkout hours and is therefore incorrect.
B) [tex]\( c = 25 + 10p + 5h \)[/tex] correctly incorporates all the terms: the base charge, the charge for additional guests, and the charge for late checkout hours.
C) [tex]\( c = 25 - 10p - 5h \)[/tex] incorrectly assumes a decrease in charges with more guests and late checkouts, which is not accurate based on Martina's pricing strategy.
D) [tex]\( c + 25 = 10p + 5h \)[/tex] re-arranges the equation incorrectly and does not represent the total charge directly.
Therefore, the correct linear equation is:
[tex]\[ \boxed{B: c = 25 + 10p + 5h} \][/tex]
