Finding the Third Proportional to 410 and 632.50

Step by Step Solution

1. Step 1: Write the proportion equation
   410 : 632.50 = 632.50 : x
2. Step 2: Convert to fraction form
   410/632.50 = 632.50/x
3. Step 3: Cross multiply
   410x = 632.50 × 632.50
4. Step 4: Simplify right side
   410x = 400,056.25
5. Step 5: Solve for x
   x = 400,056.25/410
6. Step 6: Final answer
   x = 975.75