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Finding the Third Proportional to 51,413 and 119,009

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Solution

The third proportional to 51,413 and 119,009 is: 275,477.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,413 : 119,009 = 119,009 : x
  2. Step 2: Convert to fraction form
    51,413/119,009 = 119,009/x
  3. Step 3: Cross multiply
    51,413x = 119,009 × 119,009
  4. Step 4: Simplify right side
    51,413x = 14,163,142,081
  5. Step 5: Solve for x
    x = 14,163,142,081/51,413
  6. Step 6: Final answer
    x = 275,477.84

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.