Finding the Third Proportional to 829 and 1,162.50

Step by Step Solution

1. Step 1: Write the proportion equation
   829 : 1,162.50 = 1,162.50 : x
2. Step 2: Convert to fraction form
   829/1,162.50 = 1,162.50/x
3. Step 3: Cross multiply
   829x = 1,162.50 × 1,162.50
4. Step 4: Simplify right side
   829x = 1,351,406.25
5. Step 5: Solve for x
   x = 1,351,406.25/829
6. Step 6: Final answer
   x = 1,630.16