Finding the Third Proportional to 1,536 and 1,680

Step by Step Solution

1. Step 1: Write the proportion equation
   1,536 : 1,680 = 1,680 : x
2. Step 2: Convert to fraction form
   1,536/1,680 = 1,680/x
3. Step 3: Cross multiply
   1,536x = 1,680 × 1,680
4. Step 4: Simplify right side
   1,536x = 2,822,400
5. Step 5: Solve for x
   x = 2,822,400/1,536
6. Step 6: Final answer
   x = 1,837.50