Finding the Third Proportional to 1,002 and 1,535

Step by Step Solution

1. Step 1: Write the proportion equation
   1,002 : 1,535 = 1,535 : x
2. Step 2: Convert to fraction form
   1,002/1,535 = 1,535/x
3. Step 3: Cross multiply
   1,002x = 1,535 × 1,535
4. Step 4: Simplify right side
   1,002x = 2,356,225
5. Step 5: Solve for x
   x = 2,356,225/1,002
6. Step 6: Final answer
   x = 2,351.52