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Finding the Third Proportional to 7,541 and 8,165

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Solution

The third proportional to 7,541 and 8,165 is: 8,840.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,541 : 8,165 = 8,165 : x
  2. Step 2: Convert to fraction form
    7,541/8,165 = 8,165/x
  3. Step 3: Cross multiply
    7,541x = 8,165 × 8,165
  4. Step 4: Simplify right side
    7,541x = 66,667,225
  5. Step 5: Solve for x
    x = 66,667,225/7,541
  6. Step 6: Final answer
    x = 8,840.63

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.