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Finding the Third Proportional to 175,738 and 414,460

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Solution

The third proportional to 175,738 and 414,460 is: 977,461.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    175,738 : 414,460 = 414,460 : x
  2. Step 2: Convert to fraction form
    175,738/414,460 = 414,460/x
  3. Step 3: Cross multiply
    175,738x = 414,460 × 414,460
  4. Step 4: Simplify right side
    175,738x = 171,777,091,600
  5. Step 5: Solve for x
    x = 171,777,091,600/175,738
  6. Step 6: Final answer
    x = 977,461.29

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.