Finding the Third Proportional to 456.19 and 559.69

Step by Step Solution

1. Step 1: Write the proportion equation
   456.19 : 559.69 = 559.69 : x
2. Step 2: Convert to fraction form
   456.19/559.69 = 559.69/x
3. Step 3: Cross multiply
   456.19x = 559.69 × 559.69
4. Step 4: Simplify right side
   456.19x = 313,250.10
5. Step 5: Solve for x
   x = 313,250.10/456.19
6. Step 6: Final answer
   x = 686.67