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Finding the Third Proportional to 7,677 and 9,733

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Solution

The third proportional to 7,677 and 9,733 is: 12,339.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,677 : 9,733 = 9,733 : x
  2. Step 2: Convert to fraction form
    7,677/9,733 = 9,733/x
  3. Step 3: Cross multiply
    7,677x = 9,733 × 9,733
  4. Step 4: Simplify right side
    7,677x = 94,731,289
  5. Step 5: Solve for x
    x = 94,731,289/7,677
  6. Step 6: Final answer
    x = 12,339.62

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.