Finding the Third Proportional to 410 and 577.50

Step by Step Solution

1. Step 1: Write the proportion equation
   410 : 577.50 = 577.50 : x
2. Step 2: Convert to fraction form
   410/577.50 = 577.50/x
3. Step 3: Cross multiply
   410x = 577.50 × 577.50
4. Step 4: Simplify right side
   410x = 333,506.25
5. Step 5: Solve for x
   x = 333,506.25/410
6. Step 6: Final answer
   x = 813.43