Finding the Third Proportional to 523.50 and 706.50

Step by Step Solution

1. Step 1: Write the proportion equation
   523.50 : 706.50 = 706.50 : x
2. Step 2: Convert to fraction form
   523.50/706.50 = 706.50/x
3. Step 3: Cross multiply
   523.50x = 706.50 × 706.50
4. Step 4: Simplify right side
   523.50x = 499,142.25
5. Step 5: Solve for x
   x = 499,142.25/523.50
6. Step 6: Final answer
   x = 953.47