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Finding the Third Proportional to 6,838 and 7,478

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Solution

The third proportional to 6,838 and 7,478 is: 8,177.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,838 : 7,478 = 7,478 : x
  2. Step 2: Convert to fraction form
    6,838/7,478 = 7,478/x
  3. Step 3: Cross multiply
    6,838x = 7,478 × 7,478
  4. Step 4: Simplify right side
    6,838x = 55,920,484
  5. Step 5: Solve for x
    x = 55,920,484/6,838
  6. Step 6: Final answer
    x = 8,177.90

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.