At a certain amusement park, there is a bulk discount for tickets. If you buy up to 60 tickets in one order, the price for each ticket is $70. However if you buy more than 60 tickets in a single order, the price of every ticket is reduced by $1 for each additional ticket bought. If *t* is the number of tickets bought in bulk at one time, what is the largest *t* which will bring the amusement park a profit greater than $4200?

Guest Jun 16, 2018

#1**+1 **

t = number of tickets

70 - (t-60) = price of tickets

t (70-(t-60)) >4200

t(-t +130) > 4200

-t^2 + 130t -4200 > 0

t^2-130t+4200< 0 Use Quadratic formula to find zeroes at t = 60 70

When t = 60 Sales 4200

When t = 70 sales = 4200 The question asks for the greatest number to be MORE than 4200 that would be when t = 69 Sales= 4209

Here is a graph:

ElectricPavlov
Jun 17, 2018