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Finding the Third Proportional to 7,842 and 8,738

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Solution

The third proportional to 7,842 and 8,738 is: 9,736.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,842 : 8,738 = 8,738 : x
  2. Step 2: Convert to fraction form
    7,842/8,738 = 8,738/x
  3. Step 3: Cross multiply
    7,842x = 8,738 × 8,738
  4. Step 4: Simplify right side
    7,842x = 76,352,644
  5. Step 5: Solve for x
    x = 76,352,644/7,842
  6. Step 6: Final answer
    x = 9,736.37

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.