Finding the Third Proportional to 1,001.50 and 1,537.25

Step by Step Solution

1. Step 1: Write the proportion equation
   1,001.50 : 1,537.25 = 1,537.25 : x
2. Step 2: Convert to fraction form
   1,001.50/1,537.25 = 1,537.25/x
3. Step 3: Cross multiply
   1,001.50x = 1,537.25 × 1,537.25
4. Step 4: Simplify right side
   1,001.50x = 2,363,137.56
5. Step 5: Solve for x
   x = 2,363,137.56/1,001.50
6. Step 6: Final answer
   x = 2,359.60