Finding the Third Proportional to 8,140 and 17,534

Step by Step Solution

1. Step 1: Write the proportion equation
   8,140 : 17,534 = 17,534 : x
2. Step 2: Convert to fraction form
   8,140/17,534 = 17,534/x
3. Step 3: Cross multiply
   8,140x = 17,534 × 17,534
4. Step 4: Simplify right side
   8,140x = 307,441,156
5. Step 5: Solve for x
   x = 307,441,156/8,140
6. Step 6: Final answer
   x = 37,769.18