Finding the Third Proportional to 782 and 1,077.50

Step by Step Solution

1. Step 1: Write the proportion equation
   782 : 1,077.50 = 1,077.50 : x
2. Step 2: Convert to fraction form
   782/1,077.50 = 1,077.50/x
3. Step 3: Cross multiply
   782x = 1,077.50 × 1,077.50
4. Step 4: Simplify right side
   782x = 1,161,006.25
5. Step 5: Solve for x
   x = 1,161,006.25/782
6. Step 6: Final answer
   x = 1,484.66