Finding the Third Proportional to 2,427.50 and 3,686.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,427.50 : 3,686.50 = 3,686.50 : x
2. Step 2: Convert to fraction form
   2,427.50/3,686.50 = 3,686.50/x
3. Step 3: Cross multiply
   2,427.50x = 3,686.50 × 3,686.50
4. Step 4: Simplify right side
   2,427.50x = 13,590,282.25
5. Step 5: Solve for x
   x = 13,590,282.25/2,427.50
6. Step 6: Final answer
   x = 5,598.47