Finding the Third Proportional to 1,192.50 and 1,829.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,192.50 : 1,829.50 = 1,829.50 : x
2. Step 2: Convert to fraction form
   1,192.50/1,829.50 = 1,829.50/x
3. Step 3: Cross multiply
   1,192.50x = 1,829.50 × 1,829.50
4. Step 4: Simplify right side
   1,192.50x = 3,347,070.25
5. Step 5: Solve for x
   x = 3,347,070.25/1,192.50
6. Step 6: Final answer
   x = 2,806.77