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Finding the Third Proportional to 10,784 and 15,814

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Solution

The third proportional to 10,784 and 15,814 is: 23,190.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,784 : 15,814 = 15,814 : x
  2. Step 2: Convert to fraction form
    10,784/15,814 = 15,814/x
  3. Step 3: Cross multiply
    10,784x = 15,814 × 15,814
  4. Step 4: Simplify right side
    10,784x = 250,082,596
  5. Step 5: Solve for x
    x = 250,082,596/10,784
  6. Step 6: Final answer
    x = 23,190.15

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.