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Finding the Third Proportional to 5,206 and 7,767

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Solution

The third proportional to 5,206 and 7,767 is: 11,587.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,206 : 7,767 = 7,767 : x
  2. Step 2: Convert to fraction form
    5,206/7,767 = 7,767/x
  3. Step 3: Cross multiply
    5,206x = 7,767 × 7,767
  4. Step 4: Simplify right side
    5,206x = 60,326,289
  5. Step 5: Solve for x
    x = 60,326,289/5,206
  6. Step 6: Final answer
    x = 11,587.84

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.