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Finding the Third Proportional to 6,414 and 7,278

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Solution

The third proportional to 6,414 and 7,278 is: 8,258.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,414 : 7,278 = 7,278 : x
  2. Step 2: Convert to fraction form
    6,414/7,278 = 7,278/x
  3. Step 3: Cross multiply
    6,414x = 7,278 × 7,278
  4. Step 4: Simplify right side
    6,414x = 52,969,284
  5. Step 5: Solve for x
    x = 52,969,284/6,414
  6. Step 6: Final answer
    x = 8,258.39

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.