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Finding the Third Proportional to 412.69 and 489.19

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Solution

The third proportional to 412.69 and 489.19 is: 579.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.69 : 489.19 = 489.19 : x
  2. Step 2: Convert to fraction form
    412.69/489.19 = 489.19/x
  3. Step 3: Cross multiply
    412.69x = 489.19 × 489.19
  4. Step 4: Simplify right side
    412.69x = 239,304.41
  5. Step 5: Solve for x
    x = 239,304.41/412.69
  6. Step 6: Final answer
    x = 579.87

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Why These Related Problems?

These problems maintain the same ratio (1.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.