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Finding the Third Proportional to 6,434 and 9,706

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Solution

The third proportional to 6,434 and 9,706 is: 14,641.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,434 : 9,706 = 9,706 : x
  2. Step 2: Convert to fraction form
    6,434/9,706 = 9,706/x
  3. Step 3: Cross multiply
    6,434x = 9,706 × 9,706
  4. Step 4: Simplify right side
    6,434x = 94,206,436
  5. Step 5: Solve for x
    x = 94,206,436/6,434
  6. Step 6: Final answer
    x = 14,641.97

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.