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Finding the Third Proportional to 7,802 and 12,413

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Solution

The third proportional to 7,802 and 12,413 is: 19,749.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,802 : 12,413 = 12,413 : x
  2. Step 2: Convert to fraction form
    7,802/12,413 = 12,413/x
  3. Step 3: Cross multiply
    7,802x = 12,413 × 12,413
  4. Step 4: Simplify right side
    7,802x = 154,082,569
  5. Step 5: Solve for x
    x = 154,082,569/7,802
  6. Step 6: Final answer
    x = 19,749.11

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.