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Finding the Third Proportional to 14,509 and 19,577

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Solution

The third proportional to 14,509 and 19,577 is: 26,415.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,509 : 19,577 = 19,577 : x
  2. Step 2: Convert to fraction form
    14,509/19,577 = 19,577/x
  3. Step 3: Cross multiply
    14,509x = 19,577 × 19,577
  4. Step 4: Simplify right side
    14,509x = 383,258,929
  5. Step 5: Solve for x
    x = 383,258,929/14,509
  6. Step 6: Final answer
    x = 26,415.25

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.