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Finding the Third Proportional to 6,931 and 8,419

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Solution

The third proportional to 6,931 and 8,419 is: 10,226.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,931 : 8,419 = 8,419 : x
  2. Step 2: Convert to fraction form
    6,931/8,419 = 8,419/x
  3. Step 3: Cross multiply
    6,931x = 8,419 × 8,419
  4. Step 4: Simplify right side
    6,931x = 70,879,561
  5. Step 5: Solve for x
    x = 70,879,561/6,931
  6. Step 6: Final answer
    x = 10,226.46

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.