Finding the Third Proportional to 827.50 and 1,776.25

Step by Step Solution

1. Step 1: Write the proportion equation
   827.50 : 1,776.25 = 1,776.25 : x
2. Step 2: Convert to fraction form
   827.50/1,776.25 = 1,776.25/x
3. Step 3: Cross multiply
   827.50x = 1,776.25 × 1,776.25
4. Step 4: Simplify right side
   827.50x = 3,155,064.06
5. Step 5: Solve for x
   x = 3,155,064.06/827.50
6. Step 6: Final answer
   x = 3,812.77