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Finding the Third Proportional to 9,786 and 16,097

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Solution

The third proportional to 9,786 and 16,097 is: 26,477.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,786 : 16,097 = 16,097 : x
  2. Step 2: Convert to fraction form
    9,786/16,097 = 16,097/x
  3. Step 3: Cross multiply
    9,786x = 16,097 × 16,097
  4. Step 4: Simplify right side
    9,786x = 259,113,409
  5. Step 5: Solve for x
    x = 259,113,409/9,786
  6. Step 6: Final answer
    x = 26,477.97

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.