Finding the Third Proportional to 1,005.75 and 1,523.53

Step by Step Solution

1. Step 1: Write the proportion equation
   1,005.75 : 1,523.53 = 1,523.53 : x
2. Step 2: Convert to fraction form
   1,005.75/1,523.53 = 1,523.53/x
3. Step 3: Cross multiply
   1,005.75x = 1,523.53 × 1,523.53
4. Step 4: Simplify right side
   1,005.75x = 2,321,147.47
5. Step 5: Solve for x
   x = 2,321,147.47/1,005.75
6. Step 6: Final answer
   x = 2,307.88