Finding the Third Proportional to 3,580 and 5,419.50

Step by Step Solution

1. Step 1: Write the proportion equation
   3,580 : 5,419.50 = 5,419.50 : x
2. Step 2: Convert to fraction form
   3,580/5,419.50 = 5,419.50/x
3. Step 3: Cross multiply
   3,580x = 5,419.50 × 5,419.50
4. Step 4: Simplify right side
   3,580x = 29,370,980.25
5. Step 5: Solve for x
   x = 29,370,980.25/3,580
6. Step 6: Final answer
   x = 8,204.18