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Finding the Third Proportional to 9,677 and 13,057

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Solution

The third proportional to 9,677 and 13,057 is: 17,617.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,677 : 13,057 = 13,057 : x
  2. Step 2: Convert to fraction form
    9,677/13,057 = 13,057/x
  3. Step 3: Cross multiply
    9,677x = 13,057 × 13,057
  4. Step 4: Simplify right side
    9,677x = 170,485,249
  5. Step 5: Solve for x
    x = 170,485,249/9,677
  6. Step 6: Final answer
    x = 17,617.57

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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.