Finding the Third Proportional to 380,076 and 513,040

Step by Step Solution

1. Step 1: Write the proportion equation
   380,076 : 513,040 = 513,040 : x
2. Step 2: Convert to fraction form
   380,076/513,040 = 513,040/x
3. Step 3: Cross multiply
   380,076x = 513,040 × 513,040
4. Step 4: Simplify right side
   380,076x = 263,210,041,600
5. Step 5: Solve for x
   x = 263,210,041,600/380,076
6. Step 6: Final answer
   x = 692,519.50