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Finding the Third Proportional to 5,309 and 6,494

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Solution

The third proportional to 5,309 and 6,494 is: 7,943.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,309 : 6,494 = 6,494 : x
  2. Step 2: Convert to fraction form
    5,309/6,494 = 6,494/x
  3. Step 3: Cross multiply
    5,309x = 6,494 × 6,494
  4. Step 4: Simplify right side
    5,309x = 42,172,036
  5. Step 5: Solve for x
    x = 42,172,036/5,309
  6. Step 6: Final answer
    x = 7,943.50

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.