A theather charges $50 per ticket for sets in section A, $30 per ticket for seats in section B, and $20 per ticket for seats in section C. For one play, 4000 tickets wre sold for a total of $120,000 in revenue. If 1000 more tickets in section B were sold than the other two sections combined, how many tickets in each section were sold? Solution Let tickets sold in A = x and tickets sold in C = y Tickets sold in B =1000+x+y we have x+y+x+y+1000 = 4000 ==> x+y = 1500 ==> x = 1500-y 50*x+30*(x+y+1000) + 20*y = 120000 80x+50y = 120000-30000 8x+5y = 9000 8(1500-y) + 5y = 9000 12000 - 3y = 9000 3y = 3000 y =1000 x = 500 tickets sold in A = 500 tickets sold in B = 2500 tickets sold in C = 1000 .

1. A theather charges $50 per ticket for sets in section A, $30 per ticket for seats in section B, and
$20 per ticket for seats in section C. For one play, 4000 tickets wre sold for a total of $120,000 in
revenue. If 1000 more tickets in section B were sold than the other two sections combined, how
many tickets in each section were sold?
Solution
Let tickets sold in A = x
and tickets sold in C = y
Tickets sold in B =1000+x+y
we have
x+y+x+y+1000 = 4000 ==> x+y = 1500 ==> x = 1500-y
50*x+30*(x+y+1000) + 20*y = 120000
80x+50y = 120000-30000
8x+5y = 9000
8(1500-y) + 5y = 9000
12000 - 3y = 9000
3y = 3000
y =1000
x = 500
tickets sold in A = 500
tickets sold in B = 2500

2. tickets sold in C = 1000