Finding the Third Proportional to 7,780 and 10,374

Step by Step Solution

1. Step 1: Write the proportion equation
   7,780 : 10,374 = 10,374 : x
2. Step 2: Convert to fraction form
   7,780/10,374 = 10,374/x
3. Step 3: Cross multiply
   7,780x = 10,374 × 10,374
4. Step 4: Simplify right side
   7,780x = 107,619,876
5. Step 5: Solve for x
   x = 107,619,876/7,780
6. Step 6: Final answer
   x = 13,832.89