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Finding the Third Proportional to 27,209 and 38,514

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Solution

The third proportional to 27,209 and 38,514 is: 54,516.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,209 : 38,514 = 38,514 : x
  2. Step 2: Convert to fraction form
    27,209/38,514 = 38,514/x
  3. Step 3: Cross multiply
    27,209x = 38,514 × 38,514
  4. Step 4: Simplify right side
    27,209x = 1,483,328,196
  5. Step 5: Solve for x
    x = 1,483,328,196/27,209
  6. Step 6: Final answer
    x = 54,516.09

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.