Finding the Third Proportional to 2,082 and 2,527.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,082 : 2,527.50 = 2,527.50 : x
2. Step 2: Convert to fraction form
   2,082/2,527.50 = 2,527.50/x
3. Step 3: Cross multiply
   2,082x = 2,527.50 × 2,527.50
4. Step 4: Simplify right side
   2,082x = 6,388,256.25
5. Step 5: Solve for x
   x = 6,388,256.25/2,082
6. Step 6: Final answer
   x = 3,068.33