Finding the Third Proportional to 37,601 and 82,586

Step by Step Solution

1. Step 1: Write the proportion equation
   37,601 : 82,586 = 82,586 : x
2. Step 2: Convert to fraction form
   37,601/82,586 = 82,586/x
3. Step 3: Cross multiply
   37,601x = 82,586 × 82,586
4. Step 4: Simplify right side
   37,601x = 6,820,447,396
5. Step 5: Solve for x
   x = 6,820,447,396/37,601
6. Step 6: Final answer
   x = 181,390.05