Finding the Third Proportional to 1,584 and 3,478.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,584 : 3,478.50 = 3,478.50 : x
2. Step 2: Convert to fraction form
   1,584/3,478.50 = 3,478.50/x
3. Step 3: Cross multiply
   1,584x = 3,478.50 × 3,478.50
4. Step 4: Simplify right side
   1,584x = 12,099,962.25
5. Step 5: Solve for x
   x = 12,099,962.25/1,584
6. Step 6: Final answer
   x = 7,638.87