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Finding the Third Proportional to 6,023 and 6,563

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Solution

The third proportional to 6,023 and 6,563 is: 7,151.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,023 : 6,563 = 6,563 : x
  2. Step 2: Convert to fraction form
    6,023/6,563 = 6,563/x
  3. Step 3: Cross multiply
    6,023x = 6,563 × 6,563
  4. Step 4: Simplify right side
    6,023x = 43,072,969
  5. Step 5: Solve for x
    x = 43,072,969/6,023
  6. Step 6: Final answer
    x = 7,151.41

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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.