Finding the Third Proportional to 3,829 and 5,752.50

Step by Step Solution

1. Step 1: Write the proportion equation
   3,829 : 5,752.50 = 5,752.50 : x
2. Step 2: Convert to fraction form
   3,829/5,752.50 = 5,752.50/x
3. Step 3: Cross multiply
   3,829x = 5,752.50 × 5,752.50
4. Step 4: Simplify right side
   3,829x = 33,091,256.25
5. Step 5: Solve for x
   x = 33,091,256.25/3,829
6. Step 6: Final answer
   x = 8,642.27