Finding the Third Proportional to 37,738 and 85,209

Step by Step Solution

1. Step 1: Write the proportion equation
   37,738 : 85,209 = 85,209 : x
2. Step 2: Convert to fraction form
   37,738/85,209 = 85,209/x
3. Step 3: Cross multiply
   37,738x = 85,209 × 85,209
4. Step 4: Simplify right side
   37,738x = 7,260,573,681
5. Step 5: Solve for x
   x = 7,260,573,681/37,738
6. Step 6: Final answer
   x = 192,394.24