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The image shows a problem related to supply and demand with the following parts:

### Part (a):
You are asked to provide equations for the supply and demand models using the given price and quantity data. The given demand and supply models are:

- **Demand model**: $ p = -8.4571q + 2022.0003 $
- **Supply model**: $ p = 7.4q - 232.3 $

These models are linear equations where $ p $ represents the price in dollars and $ q $ represents the quantity (in millions). You are advised not to use these rounded values for slopes and intercepts when computing equilibrium.

### Part (b):
You are required to find the price and quantity at equilibrium. The equilibrium quantity, $ q $, is already given as 142 million computers. The task is to find the equilibrium price, $ p $, which should be accurate to two decimal places and rounded to the nearest penny.

### To find the equilibrium price:
1. Set the demand equation equal to the supply equation (since at equilibrium, supply equals demand).
2. Solve for $ p $ by substituting $ q = 142 $ into either the demand or supply model.

Let me calculate the equilibrium price for you.

The equilibrium price, when the quantity is 142 million computers, is **$819.80**.

Would you like further details or have any questions about this process? 

Here are 5 related questions you might want to consider:
1. How do we derive the supply and demand equations using different points?
2. What happens if the price is above or below the equilibrium price?
3. How can we graph the supply and demand curves to visualize the equilibrium?
4. What is the significance of the slopes in supply and demand equations?
5. How would changes in the slope affect the equilibrium price?

**Tip**: When solving equilibrium problems, remember that the equilibrium price is where the supply equals demand. Solving the system of equations often requires substituting or equating the two functions.

When sold for $726.00, a desktop has an annual demand of 153 million computers and an annual supply of 129.5 million computers. When the price increases to $874.00, the demand drops to 135.5 million computers and the annual supply increases to 149.5 million computers. Provide supply and demand equations and find the equilibrium price and quantity.

Explore how to find supply and demand equations for desktop sales based on price and quantity data. Learn how to calculate equilibrium price and quantity where demand equals supply. Suitable for Grade 11-12 students.

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