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Finding the Third Proportional to 49,824 and 107,514

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Solution

The third proportional to 49,824 and 107,514 is: 232,001.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,824 : 107,514 = 107,514 : x
  2. Step 2: Convert to fraction form
    49,824/107,514 = 107,514/x
  3. Step 3: Cross multiply
    49,824x = 107,514 × 107,514
  4. Step 4: Simplify right side
    49,824x = 11,559,260,196
  5. Step 5: Solve for x
    x = 11,559,260,196/49,824
  6. Step 6: Final answer
    x = 232,001.85

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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.