Finding the Third Proportional to 37,734 and 78,569

Step by Step Solution

1. Step 1: Write the proportion equation
   37,734 : 78,569 = 78,569 : x
2. Step 2: Convert to fraction form
   37,734/78,569 = 78,569/x
3. Step 3: Cross multiply
   37,734x = 78,569 × 78,569
4. Step 4: Simplify right side
   37,734x = 6,173,087,761
5. Step 5: Solve for x
   x = 6,173,087,761/37,734
6. Step 6: Final answer
   x = 163,594.84