Finding the Third Proportional to 37,814 and 82,547

Step by Step Solution

1. Step 1: Write the proportion equation
   37,814 : 82,547 = 82,547 : x
2. Step 2: Convert to fraction form
   37,814/82,547 = 82,547/x
3. Step 3: Cross multiply
   37,814x = 82,547 × 82,547
4. Step 4: Simplify right side
   37,814x = 6,814,007,209
5. Step 5: Solve for x
   x = 6,814,007,209/37,814
6. Step 6: Final answer
   x = 180,198.00