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Finding the Third Proportional to 7,740 and 10,226

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Solution

The third proportional to 7,740 and 10,226 is: 13,510.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,740 : 10,226 = 10,226 : x
  2. Step 2: Convert to fraction form
    7,740/10,226 = 10,226/x
  3. Step 3: Cross multiply
    7,740x = 10,226 × 10,226
  4. Step 4: Simplify right side
    7,740x = 104,571,076
  5. Step 5: Solve for x
    x = 104,571,076/7,740
  6. Step 6: Final answer
    x = 13,510.47

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.