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Finding the Third Proportional to 6,464 and 7,031

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Solution

The third proportional to 6,464 and 7,031 is: 7,647.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,464 : 7,031 = 7,031 : x
  2. Step 2: Convert to fraction form
    6,464/7,031 = 7,031/x
  3. Step 3: Cross multiply
    6,464x = 7,031 × 7,031
  4. Step 4: Simplify right side
    6,464x = 49,434,961
  5. Step 5: Solve for x
    x = 49,434,961/6,464
  6. Step 6: Final answer
    x = 7,647.74

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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.