Finding the Third Proportional to 513.56 and 780.47

Step by Step Solution

1. Step 1: Write the proportion equation
   513.56 : 780.47 = 780.47 : x
2. Step 2: Convert to fraction form
   513.56/780.47 = 780.47/x
3. Step 3: Cross multiply
   513.56x = 780.47 × 780.47
4. Step 4: Simplify right side
   513.56x = 609,131.47
5. Step 5: Solve for x
   x = 609,131.47/513.56
6. Step 6: Final answer
   x = 1,186.09