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Finding the Third Proportional to 7,829 and 11,431

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Solution

The third proportional to 7,829 and 11,431 is: 16,690.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,829 : 11,431 = 11,431 : x
  2. Step 2: Convert to fraction form
    7,829/11,431 = 11,431/x
  3. Step 3: Cross multiply
    7,829x = 11,431 × 11,431
  4. Step 4: Simplify right side
    7,829x = 130,667,761
  5. Step 5: Solve for x
    x = 130,667,761/7,829
  6. Step 6: Final answer
    x = 16,690.22

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.