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Finding the Third Proportional to 284.25 and 406.13

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Solution

The third proportional to 284.25 and 406.13 is: 580.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    284.25 : 406.13 = 406.13 : x
  2. Step 2: Convert to fraction form
    284.25/406.13 = 406.13/x
  3. Step 3: Cross multiply
    284.25x = 406.13 × 406.13
  4. Step 4: Simplify right side
    284.25x = 164,937.52
  5. Step 5: Solve for x
    x = 164,937.52/284.25
  6. Step 6: Final answer
    x = 580.26

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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.