Finding the Third Proportional to 35,823 and 78,205.50

Step by Step Solution

1. Step 1: Write the proportion equation
   35,823 : 78,205.50 = 78,205.50 : x
2. Step 2: Convert to fraction form
   35,823/78,205.50 = 78,205.50/x
3. Step 3: Cross multiply
   35,823x = 78,205.50 × 78,205.50
4. Step 4: Simplify right side
   35,823x = 6,116,100,230.25
5. Step 5: Solve for x
   x = 6,116,100,230.25/35,823
6. Step 6: Final answer
   x = 170,731.10