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Finding the Third Proportional to 3,578 and 5,230

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Solution

The third proportional to 3,578 and 5,230 is: 7,644.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,578 : 5,230 = 5,230 : x
  2. Step 2: Convert to fraction form
    3,578/5,230 = 5,230/x
  3. Step 3: Cross multiply
    3,578x = 5,230 × 5,230
  4. Step 4: Simplify right side
    3,578x = 27,352,900
  5. Step 5: Solve for x
    x = 27,352,900/3,578
  6. Step 6: Final answer
    x = 7,644.75

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.