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We are given the following supply and demand functions:

- Demand function: \( P = 800 - 2Q_d \)
- Supply function: \( P = 50 + 3Q_s \)

To find the equilibrium quantity, we need to set the quantity demanded (\(Q_d\)) equal to the quantity supplied (\(Q_s\)) because, at equilibrium, demand equals supply. So, let's solve for \( Q \) by setting the two equations equal to each other:

\[
800 - 2Q = 50 + 3Q
\]

### Step-by-step Solution:

1. Combine like terms:
   \[
   800 - 50 = 3Q + 2Q
   \]
   \[
   750 = 5Q
   \]

2. Solve for \( Q \):
   \[
   Q = \frac{750}{5} = 150
   \]

Thus, the equilibrium quantity is \( Q = 150 \).

Would you like further details or clarifications? Here are some related questions for further exploration:

1. What is the equilibrium price in this market?
2. How would a shift in the demand curve affect the equilibrium?
3. How do changes in supply affect the equilibrium quantity?
4. Can you explain how supply and demand interact to form the equilibrium?
5. How is consumer surplus calculated using the demand curve?

**Tip**: When solving for equilibrium, always ensure the price equation for demand equals the price equation for supply, then solve for quantity.

For a market defined by the following supply and demand functions, what is the equilibrium quantity in this market?
Demand function: P = 800 - 2Q_d
Supply function: P = 50 + 3Q_s

This page explains how to find the equilibrium quantity for a market defined by supply and demand functions. It uses algebra to set the demand and supply equations equal to each other and solve for the quantity at equilibrium. Suitable for students in Grades 10-12.

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