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Finding the Third Proportional to 299,010 and 463,461

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Solution

The third proportional to 299,010 and 463,461 is: 718,357.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    299,010 : 463,461 = 463,461 : x
  2. Step 2: Convert to fraction form
    299,010/463,461 = 463,461/x
  3. Step 3: Cross multiply
    299,010x = 463,461 × 463,461
  4. Step 4: Simplify right side
    299,010x = 214,796,098,521
  5. Step 5: Solve for x
    x = 214,796,098,521/299,010
  6. Step 6: Final answer
    x = 718,357.58

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.