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Finding the Third Proportional to 6,565 and 7,537

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Solution

The third proportional to 6,565 and 7,537 is: 8,652.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,565 : 7,537 = 7,537 : x
  2. Step 2: Convert to fraction form
    6,565/7,537 = 7,537/x
  3. Step 3: Cross multiply
    6,565x = 7,537 × 7,537
  4. Step 4: Simplify right side
    6,565x = 56,806,369
  5. Step 5: Solve for x
    x = 56,806,369/6,565
  6. Step 6: Final answer
    x = 8,652.91

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.