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Finding the Third Proportional to 7,742 and 8,462

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Solution

The third proportional to 7,742 and 8,462 is: 9,248.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,742 : 8,462 = 8,462 : x
  2. Step 2: Convert to fraction form
    7,742/8,462 = 8,462/x
  3. Step 3: Cross multiply
    7,742x = 8,462 × 8,462
  4. Step 4: Simplify right side
    7,742x = 71,605,444
  5. Step 5: Solve for x
    x = 71,605,444/7,742
  6. Step 6: Final answer
    x = 9,248.96

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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.