How many seats does each section hold?

Question

A stadium has 54,000 seats. Seats sell for $35 in section A, $30 in section B, and $25 in section C. The number of seats in section A is equal to the number of seats in section B and section C. Suppose the stadium takes in $1,693,500 from each sold out event. How many seats does each section hold? 

 

Section A=

Section B=

Section C=

Answer 1

lets take  in stadium section A as - a seats

                              section B as - b seats

                              section C as - c seats

 

so now stadium as  total number seats equal to   a+b+c  and which is given as  54000 

 

so  a+b+c = 54000    ----eq 1

Also in the problem they stated that a = b+c  or b+c = a 

 

so substitute in eq 1  then    a+(b+c) =54000 -> a+a = 54000 

 2a= 54000 -> a = 27000

 

b+c = 27000 -> b = 27000-c

 

 

stadium takes 1,693,500 if all the seats sold out .. so amount form sectionA + amount from section B + amount from Section c = 1,693,500

 

( number seats in section A * cost of each ticket )+ ( number seats in section B* cost of each ticket) + ( number seats in section C * cost of each ticket ) = 1,693,500

 

35a+30b+25c =1,693,500     ---eq 2

 35(27000) +30(27000-c)+25c = 1,693,500

 945000 [phone]c+25c = 1,693,500

 1755000-5c=1,693,500

        5c = 61500

          c = 12300

 

Hence b = 27000-12300 = 14700

 

 

Section A= 27000

Section B= 14700

Section C= 12300