I am trying to understand the math part of supply and demand . I am not getting it,I really need help! The question is: The demand and supply functions for sweatshirts are as follows:

DEMAND Supply
Quanity Quanity
demanded(per period) supplied(/peri

price__ price
10-----15,000 $10----------22,000
9------15,500 9---------19,000
8------16,000 8---------16,000
7-------16,500 7---------13,000
6--------17,000 6--------10,000
5--------17,500 5---------7,000
4--------18,000 4---------4,000
3--------18.500 3--------1,000
2--------19,000 2--------- 0

the equation for the demand and supply functions above are as followers
Qd=20,000-500p
Qs=8,000+3000P
solve for the equilbrim price and quanity,
I donot know what to do with it.

Find where supply=demand -- from your table at price=8 Qd=16000 and Qs=16000. tada.

from you equation set Qd=Qs or 20000-500P = 8000+3000P. Solve for P (use algebra) (hint: I get P=8)
tada again, that's all there is to it.

P=8, Q=16000

P:8 And Q:16000

To find the equilibrium price and quantity, we need to determine the point at which the quantity demanded is equal to the quantity supplied. In other words, we need to find the price and quantity at which the demand and supply curves intersect.

To solve for the equilibrium price and quantity, we will set the quantity demanded equal to the quantity supplied. In this case, we have the following equations:

Quantity Demanded (Qd) = Quantity Supplied (Qs)

Qd = 20,000 - 500P
Qs = 8,000 + 3,000P

Setting Qd equal to Qs, we can rewrite the equations as:

20,000 - 500P = 8,000 + 3,000P

Now, we can solve for the equilibrium price (P):

20,000 - 500P - 8,000 = 3,000P

12,000 = 3,500P

P = 12,000 / 3,500 ≈ 3.43

Now that we have the equilibrium price, we can substitute it back into either the demand or supply equation to find the equilibrium quantity.

Using the demand equation, we substitute P = 3.43:

Qd = 20,000 - 500P
Qd = 20,000 - 500(3.43)
Qd ≈ 20,000 - 1,715
Qd ≈ 18,285

Therefore, the equilibrium price is approximately $3.43 and the equilibrium quantity is approximately 18,285 sweatshirts.