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Finding the Third Proportional to 5,776 and 6,508

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Solution

The third proportional to 5,776 and 6,508 is: 7,332.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,776 : 6,508 = 6,508 : x
  2. Step 2: Convert to fraction form
    5,776/6,508 = 6,508/x
  3. Step 3: Cross multiply
    5,776x = 6,508 × 6,508
  4. Step 4: Simplify right side
    5,776x = 42,354,064
  5. Step 5: Solve for x
    x = 42,354,064/5,776
  6. Step 6: Final answer
    x = 7,332.77

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.