Finding the Third Proportional to 1,011.75 and 1,538.63

Step by Step Solution

1. Step 1: Write the proportion equation
   1,011.75 : 1,538.63 = 1,538.63 : x
2. Step 2: Convert to fraction form
   1,011.75/1,538.63 = 1,538.63/x
3. Step 3: Cross multiply
   1,011.75x = 1,538.63 × 1,538.63
4. Step 4: Simplify right side
   1,011.75x = 2,367,366.89
5. Step 5: Solve for x
   x = 2,367,366.89/1,011.75
6. Step 6: Final answer
   x = 2,339.87