Finding the Third Proportional to 824 and 1,238.50

Step by Step Solution

1. Step 1: Write the proportion equation
   824 : 1,238.50 = 1,238.50 : x
2. Step 2: Convert to fraction form
   824/1,238.50 = 1,238.50/x
3. Step 3: Cross multiply
   824x = 1,238.50 × 1,238.50
4. Step 4: Simplify right side
   824x = 1,533,882.25
5. Step 5: Solve for x
   x = 1,533,882.25/824
6. Step 6: Final answer
   x = 1,861.51