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Finding the Third Proportional to 7,740 and 17,865

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Solution

The third proportional to 7,740 and 17,865 is: 41,234.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,740 : 17,865 = 17,865 : x
  2. Step 2: Convert to fraction form
    7,740/17,865 = 17,865/x
  3. Step 3: Cross multiply
    7,740x = 17,865 × 17,865
  4. Step 4: Simplify right side
    7,740x = 319,158,225
  5. Step 5: Solve for x
    x = 319,158,225/7,740
  6. Step 6: Final answer
    x = 41,234.91

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.