Finding the Third Proportional to 209,826 and 314,658

Step by Step Solution

1. Step 1: Write the proportion equation
   209,826 : 314,658 = 314,658 : x
2. Step 2: Convert to fraction form
   209,826/314,658 = 314,658/x
3. Step 3: Cross multiply
   209,826x = 314,658 × 314,658
4. Step 4: Simplify right side
   209,826x = 99,009,656,964
5. Step 5: Solve for x
   x = 99,009,656,964/209,826
6. Step 6: Final answer
   x = 471,865.53