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Finding the Third Proportional to 5,891 and 6,506

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Solution

The third proportional to 5,891 and 6,506 is: 7,185.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,891 : 6,506 = 6,506 : x
  2. Step 2: Convert to fraction form
    5,891/6,506 = 6,506/x
  3. Step 3: Cross multiply
    5,891x = 6,506 × 6,506
  4. Step 4: Simplify right side
    5,891x = 42,328,036
  5. Step 5: Solve for x
    x = 42,328,036/5,891
  6. Step 6: Final answer
    x = 7,185.20

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.