Finding the Third Proportional to 823 and 1,752.50

Step by Step Solution

1. Step 1: Write the proportion equation
   823 : 1,752.50 = 1,752.50 : x
2. Step 2: Convert to fraction form
   823/1,752.50 = 1,752.50/x
3. Step 3: Cross multiply
   823x = 1,752.50 × 1,752.50
4. Step 4: Simplify right side
   823x = 3,071,256.25
5. Step 5: Solve for x
   x = 3,071,256.25/823
6. Step 6: Final answer
   x = 3,731.78