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Finding the Third Proportional to 6,077 and 6,509

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Solution

The third proportional to 6,077 and 6,509 is: 6,971.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,077 : 6,509 = 6,509 : x
  2. Step 2: Convert to fraction form
    6,077/6,509 = 6,509/x
  3. Step 3: Cross multiply
    6,077x = 6,509 × 6,509
  4. Step 4: Simplify right side
    6,077x = 42,367,081
  5. Step 5: Solve for x
    x = 42,367,081/6,077
  6. Step 6: Final answer
    x = 6,971.71

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.