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Finding the Third Proportional to 5,238 and 7,413

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Solution

The third proportional to 5,238 and 7,413 is: 10,491.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,238 : 7,413 = 7,413 : x
  2. Step 2: Convert to fraction form
    5,238/7,413 = 7,413/x
  3. Step 3: Cross multiply
    5,238x = 7,413 × 7,413
  4. Step 4: Simplify right side
    5,238x = 54,952,569
  5. Step 5: Solve for x
    x = 54,952,569/5,238
  6. Step 6: Final answer
    x = 10,491.14

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.