Finding the Third Proportional to 1,002.38 and 1,535.63

Step by Step Solution

1. Step 1: Write the proportion equation
   1,002.38 : 1,535.63 = 1,535.63 : x
2. Step 2: Convert to fraction form
   1,002.38/1,535.63 = 1,535.63/x
3. Step 3: Cross multiply
   1,002.38x = 1,535.63 × 1,535.63
4. Step 4: Simplify right side
   1,002.38x = 2,358,144.14
5. Step 5: Solve for x
   x = 2,358,144.14/1,002.38
6. Step 6: Final answer
   x = 2,352.56