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Finding the Third Proportional to 2,407 and 4,002

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Solution

The third proportional to 2,407 and 4,002 is: 6,653.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,407 : 4,002 = 4,002 : x
  2. Step 2: Convert to fraction form
    2,407/4,002 = 4,002/x
  3. Step 3: Cross multiply
    2,407x = 4,002 × 4,002
  4. Step 4: Simplify right side
    2,407x = 16,016,004
  5. Step 5: Solve for x
    x = 16,016,004/2,407
  6. Step 6: Final answer
    x = 6,653.93

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.