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Finding the Third Proportional to 6,509 and 7,949

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Solution

The third proportional to 6,509 and 7,949 is: 9,707.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,509 : 7,949 = 7,949 : x
  2. Step 2: Convert to fraction form
    6,509/7,949 = 7,949/x
  3. Step 3: Cross multiply
    6,509x = 7,949 × 7,949
  4. Step 4: Simplify right side
    6,509x = 63,186,601
  5. Step 5: Solve for x
    x = 63,186,601/6,509
  6. Step 6: Final answer
    x = 9,707.57

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.