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Finding the Third Proportional to 5,038 and 6,565

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Solution

The third proportional to 5,038 and 6,565 is: 8,554.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,038 : 6,565 = 6,565 : x
  2. Step 2: Convert to fraction form
    5,038/6,565 = 6,565/x
  3. Step 3: Cross multiply
    5,038x = 6,565 × 6,565
  4. Step 4: Simplify right side
    5,038x = 43,099,225
  5. Step 5: Solve for x
    x = 43,099,225/5,038
  6. Step 6: Final answer
    x = 8,554.83

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.