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Finding the Third Proportional to 5,664 and 6,489

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Solution

The third proportional to 5,664 and 6,489 is: 7,434.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,664 : 6,489 = 6,489 : x
  2. Step 2: Convert to fraction form
    5,664/6,489 = 6,489/x
  3. Step 3: Cross multiply
    5,664x = 6,489 × 6,489
  4. Step 4: Simplify right side
    5,664x = 42,107,121
  5. Step 5: Solve for x
    x = 42,107,121/5,664
  6. Step 6: Final answer
    x = 7,434.17

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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.