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Finding the Third Proportional to 4,016 and 6,410

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Solution

The third proportional to 4,016 and 6,410 is: 10,231.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,016 : 6,410 = 6,410 : x
  2. Step 2: Convert to fraction form
    4,016/6,410 = 6,410/x
  3. Step 3: Cross multiply
    4,016x = 6,410 × 6,410
  4. Step 4: Simplify right side
    4,016x = 41,088,100
  5. Step 5: Solve for x
    x = 41,088,100/4,016
  6. Step 6: Final answer
    x = 10,231.10

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.