Finding the Third Proportional to 2,585 and 3,691.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,585 : 3,691.50 = 3,691.50 : x
2. Step 2: Convert to fraction form
   2,585/3,691.50 = 3,691.50/x
3. Step 3: Cross multiply
   2,585x = 3,691.50 × 3,691.50
4. Step 4: Simplify right side
   2,585x = 13,627,172.25
5. Step 5: Solve for x
   x = 13,627,172.25/2,585
6. Step 6: Final answer
   x = 5,271.63