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Finding the Third Proportional to 13,770 and 19,417

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Solution

The third proportional to 13,770 and 19,417 is: 27,379.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,770 : 19,417 = 19,417 : x
  2. Step 2: Convert to fraction form
    13,770/19,417 = 19,417/x
  3. Step 3: Cross multiply
    13,770x = 19,417 × 19,417
  4. Step 4: Simplify right side
    13,770x = 377,019,889
  5. Step 5: Solve for x
    x = 377,019,889/13,770
  6. Step 6: Final answer
    x = 27,379.80

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.