Round to the nearest whole number

Question

The Warbler house inn offers two plans for wedding parties . Under plan A , the inn charges $35 for each person in attendance. Under plan B the inn charges $1800 plus $20 for each person in excess to the first 35 who attend. For what size parties will plan B cost less?( Assume that more than 35 guests will attend.)

Answer 1

We need to figure out when the cost of Plan A will equal the cost of Plan B.

 

Let X = number of people in attendance.

 

The cost of plan A is $35X.

The cost of plan B is $1800 + $20(X-35) if X = 36 or greater.

 

$35X = $1800 + $20(X-35)

$35X = $1800 + $20X - $700

($35 - $20)X = $1800 - $700

$15X = $1100

X = 73.3 people. 

 

Plan A and Plan B will cost the same amount when 73.3 people attend.  Therefore, when 74 people attend, Plan B will cost less than Plan A.