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Finding the Third Proportional to 4,014 and 6,415

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Solution

The third proportional to 4,014 and 6,415 is: 10,252.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,014 : 6,415 = 6,415 : x
  2. Step 2: Convert to fraction form
    4,014/6,415 = 6,415/x
  3. Step 3: Cross multiply
    4,014x = 6,415 × 6,415
  4. Step 4: Simplify right side
    4,014x = 41,152,225
  5. Step 5: Solve for x
    x = 41,152,225/4,014
  6. Step 6: Final answer
    x = 10,252.17

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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.