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Finding the Third Proportional to 5,456 and 6,416

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Solution

The third proportional to 5,456 and 6,416 is: 7,544.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,456 : 6,416 = 6,416 : x
  2. Step 2: Convert to fraction form
    5,456/6,416 = 6,416/x
  3. Step 3: Cross multiply
    5,456x = 6,416 × 6,416
  4. Step 4: Simplify right side
    5,456x = 41,165,056
  5. Step 5: Solve for x
    x = 41,165,056/5,456
  6. Step 6: Final answer
    x = 7,544.91

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.