Finding the Third Proportional to 37,514 and 82,409.50

Step by Step Solution

1. Step 1: Write the proportion equation
   37,514 : 82,409.50 = 82,409.50 : x
2. Step 2: Convert to fraction form
   37,514/82,409.50 = 82,409.50/x
3. Step 3: Cross multiply
   37,514x = 82,409.50 × 82,409.50
4. Step 4: Simplify right side
   37,514x = 6,791,325,690.25
5. Step 5: Solve for x
   x = 6,791,325,690.25/37,514
6. Step 6: Final answer
   x = 181,034.43