Finding the Third Proportional to 830 and 1,689.50

Step by Step Solution

1. Step 1: Write the proportion equation
   830 : 1,689.50 = 1,689.50 : x
2. Step 2: Convert to fraction form
   830/1,689.50 = 1,689.50/x
3. Step 3: Cross multiply
   830x = 1,689.50 × 1,689.50
4. Step 4: Simplify right side
   830x = 2,854,410.25
5. Step 5: Solve for x
   x = 2,854,410.25/830
6. Step 6: Final answer
   x = 3,439.05