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.
Upper S left parenthesis p right parenthesis equals negative 250 plus 60 p
Upper D left parenthesis p right parenthesis equals 1100 minus 75 p
Answer parts ​(a) through ​(c).
Question content area bottom
Part 1
​(a) Find the equilibrium price for the​ T-shirts at this concert.
The equilibrium price is ​$

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To find the equilibrium price, we need to set the quantity supplied $ S(p) $ equal to the quantity demanded $ D(p) $. In equilibrium, supply equals demand:

\[
S(p) = D(p)
\]

We are given the following functions:
\[
S(p) = -250 + 60p
\]
\[
D(p) = 1100 - 75p
\]

Setting them equal to each other:
\[
-250 + 60p = 1100 - 75p
\]

Now, solve for $ p $:

1. Add $ 75p $ to both sides:
\[
-250 + 60p + 75p = 1100
\]
\[
-250 + 135p = 1100
\]

2. Add $ 250 $ to both sides:
\[
135p = 1350
\]

3. Divide by 135:
\[
p = \frac{1350}{135} = 10
\]

The equilibrium price is **$10**.

Do you want more details on this calculation, or do you have any questions?

Here are 5 related questions to think about:
1. What is the equilibrium quantity of T-shirts at the price of $10?
2. How does the supply change if the price increases by $5?
3. What happens to demand if the price decreases to $8?
4. How do shifts in demand or supply affect the equilibrium price?
5. If a tax is added to each T-shirt, how would that impact equilibrium?

**Tip:** In equilibrium, both supply and demand forces balance each other, meaning the market is in a state of rest.

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) = -250 + 60p, D(p) = 1100 - 75p. Find the equilibrium price for the​ T-shirts at this concert.

Solve for the equilibrium price of T-shirts at a concert using the supply and demand functions S(p) = -250 + 60p and D(p) = 1100 - 75p. This problem demonstrates how to set supply equal to demand, solve linear equations, and determine the market's equilibrium price. Suitable for students in Grades 10-12.

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