A baseball team plays in a stadium that holds 56,000 spectators. With ticket prices at $10, the average attendance had been 16,000. When ticket prices were lowered to $8, the average attendance rose to 24,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear. p(x)

Step-by-step explanation:

Given

Spectator or attendance

Price

When ticket price lowered by

attendance

Suppose they follow a linear relation then

where

for

For

From (i) and (ii) we get

substitute the value of m to get

Therefore the required equation becomes

i hope this is what you were looking for.

see attached graph

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal