A theatre company has 300 season tickets subscribers. The board of directors has decided to raise the price of a season ticket from the current price of $400. A survey of the subscribers has determined that, for every $20 increase in price, 10 subscribes would not renew their season tickets. Create a quadratic model(equation) and use completing the square to determine what price would maximize the revenue from the season tickets?​

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Step-by-step explanation:

A theater wants to raise the ticket by $20.

For each $20 increase they lose 10 subscribers.

At what price can they maximize the revenue?

:

Let x = no. $20 raises in price, and no. of 10 subscriber losses

:

Revenue = no. of subscribers * ticket price

r = (300-10x) * (400+20x)

FOIL

r = 120000 + 6000x - 4000x - 200x^2

A quadratic equation

r(x) = -200x^2 + 2000x + 120000

maximum occurs at the axis of symmetry, find that x = -b/(2a)

in this equation a = -200, b=2000

x = 

x = +5

:

Max revenue occurs when ticket price raise is $20 * 5 or $100 to $500

You will lose 5*10 = 50 subscribers or 250

so the revenue will be:

500 * 250 = $125,000

:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500