Question

Suppose the supply and demand for a certain textbook are given by ​supply: p equals one fourth q squared comma ​demand: p equals negative one fourth q squared plus 30 comma where p is the price and q is the quantity. Find the demand quantity and the supply quantity at a price of ​$15.

Answer 1

Answer:

the demand quantity and the supply quantity at a price of ​$15 is 8 units

Explanation:

Supply, P = 1/4 Q²

Demand, P = - 1/4 Q²+30

If P = 15

Quantity Demanded will be 15 = -0.25Q²+30;

if we move 30 across the equality sign.

Therefore -0.25Q²=-15; divide both sides by -0.25;

Q² = 60, Q = 7.746, approximately 8 units

Quantity Supplied will be 15 =  1/4 Q², dividing both sides by 1/4

Q² = 60, Q = 7.746, approximately 8.

Answer 2

Answer:

The number of books that are demanded at a price of $15 is 8

The number of books supplied at a price of $15 is 8

Explanation:

Given the supply and demand function of the textbook, p = 1/4 q2, and p = - 1/4 q2 + 30 respectively, where p and q is the price and quantity respectively,  

The quantity supplied at the price of $15 would be:

p = 1/4 q2

p = ¼ × q2

p = q2/4

15 = q2/4

15 × 4 = q2

60 = q2

q = 7.75 ≈ 8 (square root of 60)

The quantity demanded at the price of $15 would be:

p = - 1/4 q2 + 30

p = - q2/4 + 30

p – 30 = - q2/4

(p – 30) (4) = - q2

(15 – 30) (4) = - q2

( – 15) (4) = - q2

– 60 = – q2

60 = q2

q = 7.75 ≈ 8 (square root of 60)