Finding the Third Proportional to 1,003 and 1,536.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,003 : 1,536.50 = 1,536.50 : x
2. Step 2: Convert to fraction form
   1,003/1,536.50 = 1,536.50/x
3. Step 3: Cross multiply
   1,003x = 1,536.50 × 1,536.50
4. Step 4: Simplify right side
   1,003x = 2,360,832.25
5. Step 5: Solve for x
   x = 2,360,832.25/1,003
6. Step 6: Final answer
   x = 2,353.77