To find the Consumer Surplus (CS) given the demand equation \( P = 45 - 0.5Q \), and the price \( P = 32.5 \) with quantity \( Q = 25 \), we proceed with the following steps:

### Step 1: Determine the Demand Curve Intercept
The demand curve is given as:
\[
P = 45 - 0.5Q
\]
This is a linear equation with a y-intercept (maximum price consumers are willing to pay) at \( P = 45 \) when \( Q = 0 \).

### Step 2: Calculate the Price Consumers Pay at \( Q = 25 \)
You already have the price at \( Q = 25 \) as \( P = 32.5 \).

### Step 3: Calculate the Consumer Surplus (CS)
Consumer surplus is the area of the triangle formed between the demand curve and the price line at \( P = 32.5 \). This can be calculated using the formula for the area of a triangle:
\[
\text{CS} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
1. **Base**: The base is the quantity where \( Q = 25 \).
2. **Height**: The height is the difference between the maximum price consumers are willing to pay (at \( P = 45 \)) and the actual price they pay (\( P = 32.5 \)).

So:
\[
\text{Height} = 45 - 32.5 = 12.5
\]

Therefore:
\[
\text{CS} = \frac{1}{2} \times 25 \times 12.5 = \frac{1}{2} \times 312.5 = 156.25
\]

### Answer:
The Consumer Surplus (CS) is:
\[
\boxed{156.25}
\]

Would you like further details or have any questions on this?

Here are five related questions that might interest you:
1. How is Consumer Surplus affected if the demand curve slope changes?
2. What happens to Consumer Surplus if the price decreases further?
3. How can Producer Surplus be calculated in a similar scenario?
4. What is the effect on total welfare if both Consumer and Producer Surplus are maximized?
5. How would we calculate Consumer Surplus if the demand curve were non-linear?

**Tip:** To find Consumer Surplus, always visualize it as the area under the demand curve and above the price line for a clear understanding of economic welfare concepts.

The query submitted by the user: P = 45 - 0.5Q, P = 32.5, Q = 25, CS = ?

Learn how to calculate Consumer Surplus (CS) with a linear demand curve equation P = 45 - 0.5Q. This problem covers key concepts like Consumer Surplus, the geometry of triangles, and linear equations. Perfect for high school students studying economics and algebra.

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