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Finding the Third Proportional to 6,454 and 14,138

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Solution

The third proportional to 6,454 and 14,138 is: 30,970.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,454 : 14,138 = 14,138 : x
  2. Step 2: Convert to fraction form
    6,454/14,138 = 14,138/x
  3. Step 3: Cross multiply
    6,454x = 14,138 × 14,138
  4. Step 4: Simplify right side
    6,454x = 199,883,044
  5. Step 5: Solve for x
    x = 199,883,044/6,454
  6. Step 6: Final answer
    x = 30,970.41

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.