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Finding the Third Proportional to 3,206 and 7,709

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Solution

The third proportional to 3,206 and 7,709 is: 18,536.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,206 : 7,709 = 7,709 : x
  2. Step 2: Convert to fraction form
    3,206/7,709 = 7,709/x
  3. Step 3: Cross multiply
    3,206x = 7,709 × 7,709
  4. Step 4: Simplify right side
    3,206x = 59,428,681
  5. Step 5: Solve for x
    x = 59,428,681/3,206
  6. Step 6: Final answer
    x = 18,536.71

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.