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Finding the Third Proportional to 7,684 and 11,206

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Solution

The third proportional to 7,684 and 11,206 is: 16,342.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,684 : 11,206 = 11,206 : x
  2. Step 2: Convert to fraction form
    7,684/11,206 = 11,206/x
  3. Step 3: Cross multiply
    7,684x = 11,206 × 11,206
  4. Step 4: Simplify right side
    7,684x = 125,574,436
  5. Step 5: Solve for x
    x = 125,574,436/7,684
  6. Step 6: Final answer
    x = 16,342.33

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.