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Finding the Third Proportional to 7,584 and 9,876

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Solution

The third proportional to 7,584 and 9,876 is: 12,860.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,584 : 9,876 = 9,876 : x
  2. Step 2: Convert to fraction form
    7,584/9,876 = 9,876/x
  3. Step 3: Cross multiply
    7,584x = 9,876 × 9,876
  4. Step 4: Simplify right side
    7,584x = 97,535,376
  5. Step 5: Solve for x
    x = 97,535,376/7,584
  6. Step 6: Final answer
    x = 12,860.68

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.