Finding the Third Proportional to 38,376 and 83,142

Step by Step Solution

1. Step 1: Write the proportion equation
   38,376 : 83,142 = 83,142 : x
2. Step 2: Convert to fraction form
   38,376/83,142 = 83,142/x
3. Step 3: Cross multiply
   38,376x = 83,142 × 83,142
4. Step 4: Simplify right side
   38,376x = 6,912,592,164
5. Step 5: Solve for x
   x = 6,912,592,164/38,376
6. Step 6: Final answer
   x = 180,128.00