SOLUTION: An entertainment promotor for a magic show must make $161,000 from ticket sales in order to cover the cost and make a reasonable profit. The auditorium has 3000 seats with 1800 sea
Question 276777: An entertainment promotor for a magic show must make $161,000 from ticket sales in order to cover the cost and make a reasonable profit. The auditorium has 3000 seats with 1800 seats on the lower floor and 1200 balcony seats. Attendes will pay $20 more for the lower floor seats than for the balcony seats.
Write a system of equations with F for the floor seats ticket price and B for the balcony seat ticket price. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! show must make $161,000 from ticket sales in order to cover the cost and make a reasonable profit.
The auditorium has 3000 seats with 1800 seats on the lower floor and 1200 balcony seats.
Attendees will pay $20 more for the lower floor seats than for the balcony seats.
Write a system of equations with F for the floor seats ticket price and B for the balcony seat ticket price.
:
Let b = balcony price
and
f = lower floor price
f = (b+20) also
:
Total revenue equation
1200b + 1800f = 161000
:
Simplify, divide by 100
12b + 18f = 1610
:
Replace f with (b+20), find b
12b + 18(b+20) = 1610
;
12b + 18b + 360 = 1610
:
30b = 1610 - 360
b =
b = $41.67 for balcony seat
and
41.67 + 20 = $61.67 for lower floor
:
:
Check solution by finding the actual revenue
1200(41.67) + 1800(61.67) =
50004 + 111006 = $161,010.00 (an extra $10 from rounding up the cents)
