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Finding the Third Proportional to 7,709 and 15,706

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Solution

The third proportional to 7,709 and 15,706 is: 31,998.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,709 : 15,706 = 15,706 : x
  2. Step 2: Convert to fraction form
    7,709/15,706 = 15,706/x
  3. Step 3: Cross multiply
    7,709x = 15,706 × 15,706
  4. Step 4: Simplify right side
    7,709x = 246,678,436
  5. Step 5: Solve for x
    x = 246,678,436/7,709
  6. Step 6: Final answer
    x = 31,998.76

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.