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Finding the Third Proportional to 5,407 and 7,814

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Solution

The third proportional to 5,407 and 7,814 is: 11,292.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,407 : 7,814 = 7,814 : x
  2. Step 2: Convert to fraction form
    5,407/7,814 = 7,814/x
  3. Step 3: Cross multiply
    5,407x = 7,814 × 7,814
  4. Step 4: Simplify right side
    5,407x = 61,058,596
  5. Step 5: Solve for x
    x = 61,058,596/5,407
  6. Step 6: Final answer
    x = 11,292.51

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.