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Finding the Third Proportional to 6,534 and 10,397

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Solution

The third proportional to 6,534 and 10,397 is: 16,543.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,534 : 10,397 = 10,397 : x
  2. Step 2: Convert to fraction form
    6,534/10,397 = 10,397/x
  3. Step 3: Cross multiply
    6,534x = 10,397 × 10,397
  4. Step 4: Simplify right side
    6,534x = 108,097,609
  5. Step 5: Solve for x
    x = 108,097,609/6,534
  6. Step 6: Final answer
    x = 16,543.86

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.