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Finding the Third Proportional to 7,780 and 15,740

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Solution

The third proportional to 7,780 and 15,740 is: 31,844.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,780 : 15,740 = 15,740 : x
  2. Step 2: Convert to fraction form
    7,780/15,740 = 15,740/x
  3. Step 3: Cross multiply
    7,780x = 15,740 × 15,740
  4. Step 4: Simplify right side
    7,780x = 247,747,600
  5. Step 5: Solve for x
    x = 247,747,600/7,780
  6. Step 6: Final answer
    x = 31,844.16

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.