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Finding the Third Proportional to 6,514 and 7,810

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Solution

The third proportional to 6,514 and 7,810 is: 9,363.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,514 : 7,810 = 7,810 : x
  2. Step 2: Convert to fraction form
    6,514/7,810 = 7,810/x
  3. Step 3: Cross multiply
    6,514x = 7,810 × 7,810
  4. Step 4: Simplify right side
    6,514x = 60,996,100
  5. Step 5: Solve for x
    x = 60,996,100/6,514
  6. Step 6: Final answer
    x = 9,363.85

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.