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Finding the Third Proportional to 415.13 and 456.19

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Solution

The third proportional to 415.13 and 456.19 is: 501.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.13 : 456.19 = 456.19 : x
  2. Step 2: Convert to fraction form
    415.13/456.19 = 456.19/x
  3. Step 3: Cross multiply
    415.13x = 456.19 × 456.19
  4. Step 4: Simplify right side
    415.13x = 208,107.04
  5. Step 5: Solve for x
    x = 208,107.04/415.13
  6. Step 6: Final answer
    x = 501.31

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.