
Suppose that the quantity supplied S and quantity demanded D of​ T-shirts at a concert are given by the following functions where p is the price.

S(p) = -300+50p

D(p) = 960-55p

To analyze the relationship between the quantity supplied $ S(p) $ and the quantity demanded $ D(p) $ for T-shirts at a concert, we have the following functions:

- Supply function: $ S(p) = -300 + 50p $
- Demand function: $ D(p) = 960 - 55p $

### 1. **Equilibrium Price and Quantity**

The equilibrium price and quantity occur when the quantity supplied equals the quantity demanded, that is, when $ S(p) = D(p) $.

\[
-300 + 50p = 960 - 55p
\]

Now, solve for $ p $:

\[
50p + 55p = 960 + 300
\]

\[
105p = 1260
\]

\[
p = \frac{1260}{105} = 12
\]

So, the equilibrium price $ p $ is **$12**.

### 2. **Equilibrium Quantity**

Now that we know the equilibrium price, substitute $ p = 12 $ into either the supply or demand function to find the equilibrium quantity. Let’s use the supply function $ S(p) $:

\[
S(12) = -300 + 50(12)
\]

\[
S(12) = -300 + 600 = 300
\]

Thus, the equilibrium quantity is **300 T-shirts**.

### Conclusion:

- **Equilibrium price**: $12
- **Equilibrium quantity**: 300 T-shirts

Would you like further details or any clarification?

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### 5 Related Questions:

1. How does a change in price affect the supply and demand functions?
2. What happens to the equilibrium if the supply function changes to $ S(p) = -250 + 50p $?
3. How would a price ceiling below the equilibrium price affect the market for T-shirts?
4. Can you find the price at which demand is zero?
5. How would an increase in production cost impact the supply function?

**Tip**: The equilibrium price and quantity are determined where the market forces of supply and demand are perfectly balanced.

Suppose that the quantity supplied S and quantity demanded D of​ T-shirts at a concert are given by the following functions where p is the price: S(p) = -300+50p and D(p) = 960-55p.

Discover how to calculate the equilibrium price and quantity for T-shirts at a concert using the supply and demand functions S(p) = -300 + 50p and D(p) = 960 - 55p. This guide walks you through solving linear equations and determining market equilibrium, suitable for students in Grades 9-12.

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