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Finding the Third Proportional to 7,769 and 16,297

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Solution

The third proportional to 7,769 and 16,297 is: 34,186.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,769 : 16,297 = 16,297 : x
  2. Step 2: Convert to fraction form
    7,769/16,297 = 16,297/x
  3. Step 3: Cross multiply
    7,769x = 16,297 × 16,297
  4. Step 4: Simplify right side
    7,769x = 265,592,209
  5. Step 5: Solve for x
    x = 265,592,209/7,769
  6. Step 6: Final answer
    x = 34,186.15

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.