Question

7) The principal at a high school is planning a concert to raise money for the music programs. He determines

the profit p from ticket sales depends on the price of a ticket according to the equation
p = -200t2 + 3600t - 6400. All amounts are in dollars. If the goal is to raise $8500, what is the smallest
amount the school should charge for a ticket to the concert?

Answer 1

The smallest amout that the school should charge is $4.70.

Explanation:

p = -200t2 + 3600t - 6400

p = -200 x 4.7 x 2 + 3600 x 4.7 - 6400

p = -1880 + 16920 - 6400

p = 15120 - 6400

p = 8720

Answer 2

Answer: 6, 45 $

Explanation:

`\displaystyle -200t^2+3600t-6400=8500 \ \ |/100\\\\ -2t^2+36t-64-85 =0 \ \ |\cdot (-1) \\\\ 2t^2-36t+149=0 \\\\ \rm D=36^2-4\cdot2\cdot 149=104 \\\\ x_1=(36+2√(26) )/(4) \approx11,54 \\\\\\ x_2=(36-2√(26) )/(4) \approx 6,45 \\\\ x_2<x_1 \\\\ Then :\\\\ Answer : 6,45 \$`