Finding the Third Proportional to 3,584 and 5,538.50

Step by Step Solution

1. Step 1: Write the proportion equation
   3,584 : 5,538.50 = 5,538.50 : x
2. Step 2: Convert to fraction form
   3,584/5,538.50 = 5,538.50/x
3. Step 3: Cross multiply
   3,584x = 5,538.50 × 5,538.50
4. Step 4: Simplify right side
   3,584x = 30,674,982.25
5. Step 5: Solve for x
   x = 30,674,982.25/3,584
6. Step 6: Final answer
   x = 8,558.87