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Finding the Third Proportional to 6,542 and 7,082

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Solution

The third proportional to 6,542 and 7,082 is: 7,666.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,542 : 7,082 = 7,082 : x
  2. Step 2: Convert to fraction form
    6,542/7,082 = 7,082/x
  3. Step 3: Cross multiply
    6,542x = 7,082 × 7,082
  4. Step 4: Simplify right side
    6,542x = 50,154,724
  5. Step 5: Solve for x
    x = 50,154,724/6,542
  6. Step 6: Final answer
    x = 7,666.57

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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.