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Finding the Third Proportional to 397.69 and 456.19

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Solution

The third proportional to 397.69 and 456.19 is: 523.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    397.69 : 456.19 = 456.19 : x
  2. Step 2: Convert to fraction form
    397.69/456.19 = 456.19/x
  3. Step 3: Cross multiply
    397.69x = 456.19 × 456.19
  4. Step 4: Simplify right side
    397.69x = 208,107.04
  5. Step 5: Solve for x
    x = 208,107.04/397.69
  6. Step 6: Final answer
    x = 523.29

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.