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Finding the Third Proportional to 6,517 and 10,097

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Solution

The third proportional to 6,517 and 10,097 is: 15,643.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,517 : 10,097 = 10,097 : x
  2. Step 2: Convert to fraction form
    6,517/10,097 = 10,097/x
  3. Step 3: Cross multiply
    6,517x = 10,097 × 10,097
  4. Step 4: Simplify right side
    6,517x = 101,949,409
  5. Step 5: Solve for x
    x = 101,949,409/6,517
  6. Step 6: Final answer
    x = 15,643.61

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.