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polet [3.4K]
3 years ago
7

Tickets for Adults were $14.50 and tickets for Children were $9.00. We purchased 12 tickets and spent a total of $135.50 to get

into the aquarium. How many adult tickets and student tickets did we purchase?
Mathematics
2 answers:
ikadub [295]3 years ago
7 0

children tickets = 7

adult tickets = 5

a+c=135.5

14.5+c=135.5

14.5x7=72.5

135.5-72.5= 63

c=63

mihalych1998 [28]3 years ago
6 0

Answer:

(5 , 7)

Step-by-step explanation:

let a = the number of adult tickets

let c = the number of children tickets

then we have to solve the following system

a + c = 12

14.5a + 9c = 135.5

we proceed by Substitution:

              c = 12 - a

14.5a + 9c = 135.5

After some calculations we find

a=5 and c=7

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See attachment for the full question
alexandr402 [8]

The inverse of the demand function is; P = 9 - 0.25Q

The profit-maximizing price and quantity are; $8.5 and 2 units.

The maximum profit is; $1

<h3>How to find the inverse of a function?</h3>

A) The demand function we are given is;

Q = 36 - 4P

Making P the subject gives the inverse demand function;

P = (36 - Q)/4

P = 9 - Q/4

P = 9 - 0.25Q

B) The profit-maximization point is the point at which MR = MC.

MR refers to the marginal revenue and MC is the marginal cost.

MC can be calculated as the first derivative of the cost function:

C(Q) = 4 + 4Q + Q²

MC = C'(Q) = 2Q + 4

Total Revenue = Price * Quantity

Total Revenue = (9 - 0.25Q) * Q

Total Revenue = 9Q - 0.25Q²

MR is gotten by differentiating Total Revenue to get;

MR = 9 - 0.5Q

Applying the condition MR = MC, we have;

9 - 0.5Q = 4 - 2Q

Solving for Q gives Q = 2

Thus, profit maximizing quantity is 2.

Thus, profit maximizing price will be;

P(2) = 9 - 0.25(2)

P(2) = $8.5

C) Formula for Maximum Profit is;

Profit = Total Revenue - Total Cost

Total Revenue = 8.5 * 2

Total revenue = $17

Total Cost is;

C(2) = 4 + 4(2) + 2²

C(2) = $16

Thus;

Maximum Profit = 17 - 16 = $1

Read more about Inverse of a function at; brainly.com/question/13948067

#SPJ1

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