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Finding the Third Proportional to 5,978 and 6,590

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Solution

The third proportional to 5,978 and 6,590 is: 7,264.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,978 : 6,590 = 6,590 : x
  2. Step 2: Convert to fraction form
    5,978/6,590 = 6,590/x
  3. Step 3: Cross multiply
    5,978x = 6,590 × 6,590
  4. Step 4: Simplify right side
    5,978x = 43,428,100
  5. Step 5: Solve for x
    x = 43,428,100/5,978
  6. Step 6: Final answer
    x = 7,264.65

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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.