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Finding the Third Proportional to 8,460 and 9,729

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Solution

The third proportional to 8,460 and 9,729 is: 11,188.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,460 : 9,729 = 9,729 : x
  2. Step 2: Convert to fraction form
    8,460/9,729 = 9,729/x
  3. Step 3: Cross multiply
    8,460x = 9,729 × 9,729
  4. Step 4: Simplify right side
    8,460x = 94,653,441
  5. Step 5: Solve for x
    x = 94,653,441/8,460
  6. Step 6: Final answer
    x = 11,188.35

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.