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Finding the Third Proportional to 382,464 and 562,561

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Solution

The third proportional to 382,464 and 562,561 is: 827,463.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    382,464 : 562,561 = 562,561 : x
  2. Step 2: Convert to fraction form
    382,464/562,561 = 562,561/x
  3. Step 3: Cross multiply
    382,464x = 562,561 × 562,561
  4. Step 4: Simplify right side
    382,464x = 316,474,878,721
  5. Step 5: Solve for x
    x = 316,474,878,721/382,464
  6. Step 6: Final answer
    x = 827,463.18

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.