SOLUTION: I would appreciate help with the following word problem: The Arnold Inn offers two plans for wedding parties. Under plan A, the inn charges $30 for each person in attendance. Un

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Question 214180: I would appreciate help with the following word problem:
The Arnold Inn offers two plans for wedding parties. Under plan A, the inn charges $30 for each person in attendance. Under plan B, the inn charges $1300 plus $20 for each person in excess of thefirst 25 who attend. For what size parties will plan B cost less? (Assume that more than 25 guests will attend.)
Solve as an inequality. I would appreciate if you show your work so I can understand how it's done.
Thank you very, very much!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let C = the cost of the plans
Let n = number of guests
Plan A:
C+=+30n
Plan B:
C+=+1300+%2B+20%2A%28n+-+25%29
I want all situations where Plan A costs more than Plan B
30n+%3E+1300+%2B+20%2A%28n+-+25%29
30n+%3E+1300+%2B+20n+-+500
10n+%3E+800
n+%3E+80
If the number of guests is greater than 80,
plan B costs less than Plan A
check answer:
Suppose there are 80 guests
Plan A:
C+=+30%2A80
C+=+2400
Plan B:
C+=+1300+%2B+20%2A%2880+-+25%29
C+=+1300+%2B+20%2A55
C+=+1300+%2B+1100
C+=+2400 (break even point)
Suppose there are 81 guests:
Plan A:
C+=+30%2A81
C+=+2430
Plan B:
C+=+1300+%2B+20%2A%2881+-+25%29
C+=+1300+%2B+20%2A56
C+=+1300+%2B+1120
C+=+2420 ($10 cheaper)
OK