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Finding the Third Proportional to 2,408 and 2,584

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Solution

The third proportional to 2,408 and 2,584 is: 2,772.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,408 : 2,584 = 2,584 : x
  2. Step 2: Convert to fraction form
    2,408/2,584 = 2,584/x
  3. Step 3: Cross multiply
    2,408x = 2,584 × 2,584
  4. Step 4: Simplify right side
    2,408x = 6,677,056
  5. Step 5: Solve for x
    x = 6,677,056/2,408
  6. Step 6: Final answer
    x = 2,772.86

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.