**Equilibrium Price: Skateboards**   The demand for your factory-made skateboards, in weekly sales, is 

*q* = −5*p* + 50

 if the selling price is $*p*. If you are selling them at that price, you can obtain 

*q* = *p* − 30

 per week from the factory. At what price should you sell your skateboards so that there is neither a shortage nor a surplus? (Round your answer to the nearest cent.)

$

To find the equilibrium price, we need to determine the price at which the quantity demanded equals the quantity supplied. This means setting the two equations equal to each other:

Given:
1. Demand equation: $ q = -5p + 50 $
2. Supply equation: $ q = p - 30 $

### Step 1: Set the two equations equal to each other.
\[
-5p + 50 = p - 30
\]

### Step 2: Solve for $ p $.

First, let's move all terms involving $ p $ to one side:
\[
50 + 30 = p + 5p
\]
\[
80 = 6p
\]

Now, solve for $ p $:
\[
p = \frac{80}{6} \approx 13.33
\]

### Conclusion:
The equilibrium price is approximately **\$13.33**.

Would you like further clarification on any steps, or more details?

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Here are five related questions to consider:
1. How would the equilibrium price change if the demand equation had a different slope?
2. What happens to the equilibrium price if the supply equation changes to $ q = 2p - 20 $?
3. How would a price ceiling below the equilibrium price affect the skateboard market?
4. Can you compute the equilibrium quantity once you know the equilibrium price?
5. How would you interpret a situation where the equilibrium price is negative (in a theoretical case)?

**Tip:** Always double-check your solution by plugging the equilibrium price back into both the demand and supply equations to verify the results.

The demand for your factory-made skateboards, in weekly sales, is q = -5p + 50 if the selling price is $p. If you are selling them at that price, you can obtain q = p − 30 per week from the factory. At what price should you sell your skateboards so that there is neither a shortage nor a surplus? (Round your answer to the nearest cent.)

Discover how to find the equilibrium price for skateboards using algebraic methods. This problem involves solving the supply and demand equations: q = -5p + 50 and q = p - 30. Perfect for students in Grades 10-12, it offers a step-by-step solution to determine the price where there is neither a shortage nor a surplus in the market.

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