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Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges 5 dollars, 1065 people will attend. If she charges 7 dollars, 805 people will attend. How much should she charge per ticket to make the most money? (Round your answer to the nearest cent.)

Respuesta :

Answer:

Rosalle must charge $6.5961.

Explanation:

The information for the question is given as such

Cost of $5= 1065 people

Cost of $7= 805

Therefore, the points for x and y in an equation are already known

Step 1: Let x become the cost per ticket and y be the number of people

= y2-y1/x2-x1= 805-1065/7.5

= 260/2

The Slope called M= - 130

Step 2: Now use the equation y-y1= m(x-x1)

= y-1065= -130 (x-5)

= y-1065= -130x + 650

y= -130x + 1065+650

= -130x+ 1,715 = This is the linear function for y

Step 3: Now determine the total money Rosalle can earn as follows

f(x)=xy

= x(-130x + 1715)

= -130x∧w +1715x

= We can then solve for y in a quadratic equation

y= ax∧2 + bx + c

where x = -b/2a

a = 130, b= -1715 and c=0

Therefore: x = - (-1715)/2(130)= 1715/260

= 6.5961

Therefore, in order to make the most money, Rosalle must charge $6.5961.

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