A moving picture theater usually took in $220 an evening on ticket sales. The manager found out that by reducing the price of tickets by 5 cents, 200 more persons attended, and the box office receipts were $80 more an evening. How many persons attended before the reduction in price?
If there were normally x tickets sold, the price was 220/x
(220/x-.05)(x+200) = 220+80
x = 400
can you show how the equation is solved?
just like any similar equation...
(220/x-.05)(x+200) = 220+80
(220/x-.05)(x+200) = 300
(220-x/20)(x+200) = 300x
(4400-x)(x+200) = 6000x
-x^2 + 4200x + 880000 = 6000x
x^2 + 1800x - 880000 = 0
(x-400)(x+2200) = 0
To solve this problem, let's set up the given information as equations.
Let's say the original number of attendees is 'x'.
According to the given information:
1. The original ticket price was reduced by 5 cents, so the new ticket price = original price - 0.05.
2. With this reduced price, 200 more people attended, so the new number of attendees = x + 200.
3. The box office receipts increased by $80, so the new total ticket sales = $220 + $80.
Now we can set up the equations:
Original ticket sales = original ticket price * number of attendees
New ticket sales = new ticket price * new number of attendees
Equation 1: $220 = original price * x
Equation 2: ($220 + $80) = (original price - 0.05) * (x + 200)
Now we can solve these equations to find the original number of attendees (x).
From Equation 1, we can rearrange it to find the original price:
original price = $220 / x
Substituting this value in Equation 2, we get:
($220 + $80) = ($220 / x - 0.05) * (x + 200)
Now we can simplify and solve this equation for x.
I'll calculate the value of x for you.