Finding the Third Proportional to 49,584 and 75,538.50

Step by Step Solution

1. Step 1: Write the proportion equation
   49,584 : 75,538.50 = 75,538.50 : x
2. Step 2: Convert to fraction form
   49,584/75,538.50 = 75,538.50/x
3. Step 3: Cross multiply
   49,584x = 75,538.50 × 75,538.50
4. Step 4: Simplify right side
   49,584x = 5,706,064,982.25
5. Step 5: Solve for x
   x = 5,706,064,982.25/49,584
6. Step 6: Final answer
   x = 115,078.75