Finding the Third Proportional to 37,742 and 82,046

Step by Step Solution

1. Step 1: Write the proportion equation
   37,742 : 82,046 = 82,046 : x
2. Step 2: Convert to fraction form
   37,742/82,046 = 82,046/x
3. Step 3: Cross multiply
   37,742x = 82,046 × 82,046
4. Step 4: Simplify right side
   37,742x = 6,731,546,116
5. Step 5: Solve for x
   x = 6,731,546,116/37,742
6. Step 6: Final answer
   x = 178,356.90