Finding the Third Proportional to 1,537 and 2,386.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,537 : 2,386.50 = 2,386.50 : x
2. Step 2: Convert to fraction form
   1,537/2,386.50 = 2,386.50/x
3. Step 3: Cross multiply
   1,537x = 2,386.50 × 2,386.50
4. Step 4: Simplify right side
   1,537x = 5,695,382.25
5. Step 5: Solve for x
   x = 5,695,382.25/1,537
6. Step 6: Final answer
   x = 3,705.52