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Finding the Third Proportional to 289.73 and 413.06

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Solution

The third proportional to 289.73 and 413.06 is: 588.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    289.73 : 413.06 = 413.06 : x
  2. Step 2: Convert to fraction form
    289.73/413.06 = 413.06/x
  3. Step 3: Cross multiply
    289.73x = 413.06 × 413.06
  4. Step 4: Simplify right side
    289.73x = 170,620.63
  5. Step 5: Solve for x
    x = 170,620.63/289.73
  6. Step 6: Final answer
    x = 588.89

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.