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Finding the Third Proportional to 685.97 and 1,413.70

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Solution

The third proportional to 685.97 and 1,413.70 is: 2,913.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    685.97 : 1,413.70 = 1,413.70 : x
  2. Step 2: Convert to fraction form
    685.97/1,413.70 = 1,413.70/x
  3. Step 3: Cross multiply
    685.97x = 1,413.70 × 1,413.70
  4. Step 4: Simplify right side
    685.97x = 1,998,556.53
  5. Step 5: Solve for x
    x = 1,998,556.53/685.97
  6. Step 6: Final answer
    x = 2,913.48

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.