Finding the Third Proportional to 3,178 and 3,659.50

Step by Step Solution

1. Step 1: Write the proportion equation
   3,178 : 3,659.50 = 3,659.50 : x
2. Step 2: Convert to fraction form
   3,178/3,659.50 = 3,659.50/x
3. Step 3: Cross multiply
   3,178x = 3,659.50 × 3,659.50
4. Step 4: Simplify right side
   3,178x = 13,391,940.25
5. Step 5: Solve for x
   x = 13,391,940.25/3,178
6. Step 6: Final answer
   x = 4,213.95