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Finding the Third Proportional to 3,578 and 6,424

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Solution

The third proportional to 3,578 and 6,424 is: 11,533.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,578 : 6,424 = 6,424 : x
  2. Step 2: Convert to fraction form
    3,578/6,424 = 6,424/x
  3. Step 3: Cross multiply
    3,578x = 6,424 × 6,424
  4. Step 4: Simplify right side
    3,578x = 41,267,776
  5. Step 5: Solve for x
    x = 41,267,776/3,578
  6. Step 6: Final answer
    x = 11,533.76

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Why These Related Problems?

These problems maintain the same ratio (1.80) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.