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Finding the Third Proportional to 6,410 and 8,642

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Solution

The third proportional to 6,410 and 8,642 is: 11,651.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,410 : 8,642 = 8,642 : x
  2. Step 2: Convert to fraction form
    6,410/8,642 = 8,642/x
  3. Step 3: Cross multiply
    6,410x = 8,642 × 8,642
  4. Step 4: Simplify right side
    6,410x = 74,684,164
  5. Step 5: Solve for x
    x = 74,684,164/6,410
  6. Step 6: Final answer
    x = 11,651.20

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.