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Finding the Third Proportional to 6,503 and 7,421

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Solution

The third proportional to 6,503 and 7,421 is: 8,468.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,503 : 7,421 = 7,421 : x
  2. Step 2: Convert to fraction form
    6,503/7,421 = 7,421/x
  3. Step 3: Cross multiply
    6,503x = 7,421 × 7,421
  4. Step 4: Simplify right side
    6,503x = 55,071,241
  5. Step 5: Solve for x
    x = 55,071,241/6,503
  6. Step 6: Final answer
    x = 8,468.59

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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.