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Finding the Third Proportional to 5,664 and 6,456

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Solution

The third proportional to 5,664 and 6,456 is: 7,358.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,664 : 6,456 = 6,456 : x
  2. Step 2: Convert to fraction form
    5,664/6,456 = 6,456/x
  3. Step 3: Cross multiply
    5,664x = 6,456 × 6,456
  4. Step 4: Simplify right side
    5,664x = 41,679,936
  5. Step 5: Solve for x
    x = 41,679,936/5,664
  6. Step 6: Final answer
    x = 7,358.75

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.