Finding the Third Proportional to 27,824 and 42,657

Step by Step Solution

1. Step 1: Write the proportion equation
   27,824 : 42,657 = 42,657 : x
2. Step 2: Convert to fraction form
   27,824/42,657 = 42,657/x
3. Step 3: Cross multiply
   27,824x = 42,657 × 42,657
4. Step 4: Simplify right side
   27,824x = 1,819,619,649
5. Step 5: Solve for x
   x = 1,819,619,649/27,824
6. Step 6: Final answer
   x = 65,397.49