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Finding the Third Proportional to 8,298 and 9,738

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Solution

The third proportional to 8,298 and 9,738 is: 11,427.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,298 : 9,738 = 9,738 : x
  2. Step 2: Convert to fraction form
    8,298/9,738 = 9,738/x
  3. Step 3: Cross multiply
    8,298x = 9,738 × 9,738
  4. Step 4: Simplify right side
    8,298x = 94,828,644
  5. Step 5: Solve for x
    x = 94,828,644/8,298
  6. Step 6: Final answer
    x = 11,427.89

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.