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Finding the Third Proportional to 260,577 and 412,947

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Solution

The third proportional to 260,577 and 412,947 is: 654,413.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    260,577 : 412,947 = 412,947 : x
  2. Step 2: Convert to fraction form
    260,577/412,947 = 412,947/x
  3. Step 3: Cross multiply
    260,577x = 412,947 × 412,947
  4. Step 4: Simplify right side
    260,577x = 170,525,224,809
  5. Step 5: Solve for x
    x = 170,525,224,809/260,577
  6. Step 6: Final answer
    x = 654,413.95

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.