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Finding the Third Proportional to 5,642 and 13,577

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Solution

The third proportional to 5,642 and 13,577 is: 32,671.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,642 : 13,577 = 13,577 : x
  2. Step 2: Convert to fraction form
    5,642/13,577 = 13,577/x
  3. Step 3: Cross multiply
    5,642x = 13,577 × 13,577
  4. Step 4: Simplify right side
    5,642x = 184,334,929
  5. Step 5: Solve for x
    x = 184,334,929/5,642
  6. Step 6: Final answer
    x = 32,671.91

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.