Finding the Third Proportional to 412.50 and 802.50

Step by Step Solution

1. Step 1: Write the proportion equation
   412.50 : 802.50 = 802.50 : x
2. Step 2: Convert to fraction form
   412.50/802.50 = 802.50/x
3. Step 3: Cross multiply
   412.50x = 802.50 × 802.50
4. Step 4: Simplify right side
   412.50x = 644,006.25
5. Step 5: Solve for x
   x = 644,006.25/412.50
6. Step 6: Final answer
   x = 1,561.23