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Finding the Third Proportional to 5,709 and 6,546

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Solution

The third proportional to 5,709 and 6,546 is: 7,505.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,709 : 6,546 = 6,546 : x
  2. Step 2: Convert to fraction form
    5,709/6,546 = 6,546/x
  3. Step 3: Cross multiply
    5,709x = 6,546 × 6,546
  4. Step 4: Simplify right side
    5,709x = 42,850,116
  5. Step 5: Solve for x
    x = 42,850,116/5,709
  6. Step 6: Final answer
    x = 7,505.71

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.