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Finding the Third Proportional to 51,691 and 77,537

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Solution

The third proportional to 51,691 and 77,537 is: 116,306.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,691 : 77,537 = 77,537 : x
  2. Step 2: Convert to fraction form
    51,691/77,537 = 77,537/x
  3. Step 3: Cross multiply
    51,691x = 77,537 × 77,537
  4. Step 4: Simplify right side
    51,691x = 6,011,986,369
  5. Step 5: Solve for x
    x = 6,011,986,369/51,691
  6. Step 6: Final answer
    x = 116,306.25

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These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.