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To solve this problem, we need to find the price \( P \) at which the total quantity supplied is 250 units, given the supply functions for two producers.

The supply functions are:
- Supply 1: \( P = 3 + 1.3Q_1 \)
- Supply 2: \( P = 15 + 0.7Q_2 \)

The total quantity supplied \( Q \) is given by:
\[ Q = Q_1 + Q_2 = 250 \]

We need to express \( Q_1 \) and \( Q_2 \) in terms of \( P \), and then solve for \( P \) when \( Q_1 + Q_2 = 250 \).

1. **Rearrange the supply functions to solve for \( Q_1 \) and \( Q_2 \):**
   \[
   Q_1 = \frac{P - 3}{1.3}
   \]
   \[
   Q_2 = \frac{P - 15}{0.7}
   \]

2. **Set up the equation for total quantity supplied:**
   \[
   Q_1 + Q_2 = 250
   \]
   Substitute the expressions for \( Q_1 \) and \( Q_2 \):
   \[
   \frac{P - 3}{1.3} + \frac{P - 15}{0.7} = 250
   \]

3. **Clear the denominators by multiplying through by 1.3 and 0.7:**
   \[
   0.7(P - 3) + 1.3(P - 15) = 250 \cdot 1.3 \cdot 0.7
   \]
   \[
   0.7P - 2.1 + 1.3P - 19.5 = 250 \cdot 0.91
   \]
   \[
   2P - 21.6 = 227.5
   \]

4. **Solve for \( P \):**
   \[
   2P = 249.1 + 21.6
   \]
   \[
   2P = 249.1 + 21.6
   \]
   \[
   2P = 249.1
   \]
   \[
   P = \frac{249.1}{2}
   \]
   \[
   P = 124.55
   \]

Therefore, the price at which the total quantity supplied is 250 units is \( \boxed{124.55} \).

Would you like more details or have any questions?

Here are some related questions you might consider:
1. How do you derive the supply function from given market data?
2. What are the implications of different slopes in the supply functions?
3. How would changes in the supply functions affect the equilibrium price?
4. What is the significance of the intercept in the supply function?
5. How can supply functions be used to predict market behavior?

**Tip:** When solving supply and demand problems, always start by isolating variables and carefully manage algebraic manipulation to avoid mistakes.

Suppose there are two producers in a market with the following supply functions: Supply 1: P = 3 + 1.3Q and Supply 2: P = 15 + 0.7Q. When the price is [Answer], the total quantity supplied is 250. (In decimal numbers, with two decimal places, please.)

Learn how to calculate the price where the total quantity supplied equals 250 using two supply functions in a market. This detailed step-by-step solution explains how to solve linear equations involving supply and demand. Suitable for Grades 10-12.

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