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Finding the Third Proportional to 214.69 and 463.69

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Solution

The third proportional to 214.69 and 463.69 is: 1,001.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.69 : 463.69 = 463.69 : x
  2. Step 2: Convert to fraction form
    214.69/463.69 = 463.69/x
  3. Step 3: Cross multiply
    214.69x = 463.69 × 463.69
  4. Step 4: Simplify right side
    214.69x = 215,006.10
  5. Step 5: Solve for x
    x = 215,006.10/214.69
  6. Step 6: Final answer
    x = 1,001.48

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.