Finding the Third Proportional to 7,824 and 10,338

Step by Step Solution

1. Step 1: Write the proportion equation
   7,824 : 10,338 = 10,338 : x
2. Step 2: Convert to fraction form
   7,824/10,338 = 10,338/x
3. Step 3: Cross multiply
   7,824x = 10,338 × 10,338
4. Step 4: Simplify right side
   7,824x = 106,874,244
5. Step 5: Solve for x
   x = 106,874,244/7,824
6. Step 6: Final answer
   x = 13,659.80