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Finding the Third Proportional to 414 and 472

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Solution

The third proportional to 414 and 472 is: 538.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 472 = 472 : x
  2. Step 2: Convert to fraction form
    414/472 = 472/x
  3. Step 3: Cross multiply
    414x = 472 × 472
  4. Step 4: Simplify right side
    414x = 222,784
  5. Step 5: Solve for x
    x = 222,784/414
  6. Step 6: Final answer
    x = 538.13

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.