Finding the Third Proportional to 83,178 and 116,409

Step by Step Solution

1. Step 1: Write the proportion equation
   83,178 : 116,409 = 116,409 : x
2. Step 2: Convert to fraction form
   83,178/116,409 = 116,409/x
3. Step 3: Cross multiply
   83,178x = 116,409 × 116,409
4. Step 4: Simplify right side
   83,178x = 13,551,055,281
5. Step 5: Solve for x
   x = 13,551,055,281/83,178
6. Step 6: Final answer
   x = 162,916.34