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Finding the Third Proportional to 6,419 and 7,346

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Solution

The third proportional to 6,419 and 7,346 is: 8,406.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,419 : 7,346 = 7,346 : x
  2. Step 2: Convert to fraction form
    6,419/7,346 = 7,346/x
  3. Step 3: Cross multiply
    6,419x = 7,346 × 7,346
  4. Step 4: Simplify right side
    6,419x = 53,963,716
  5. Step 5: Solve for x
    x = 53,963,716/6,419
  6. Step 6: Final answer
    x = 8,406.87

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.