Finding the Third Proportional to 2,588.63 and 4,117.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,588.63 : 4,117.50 = 4,117.50 : x
2. Step 2: Convert to fraction form
   2,588.63/4,117.50 = 4,117.50/x
3. Step 3: Cross multiply
   2,588.63x = 4,117.50 × 4,117.50
4. Step 4: Simplify right side
   2,588.63x = 16,953,806.25
5. Step 5: Solve for x
   x = 16,953,806.25/2,588.63
6. Step 6: Final answer
   x = 6,549.35