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Finding the Third Proportional to 4,077 and 7,830

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Solution

The third proportional to 4,077 and 7,830 is: 15,037.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,077 : 7,830 = 7,830 : x
  2. Step 2: Convert to fraction form
    4,077/7,830 = 7,830/x
  3. Step 3: Cross multiply
    4,077x = 7,830 × 7,830
  4. Step 4: Simplify right side
    4,077x = 61,308,900
  5. Step 5: Solve for x
    x = 61,308,900/4,077
  6. Step 6: Final answer
    x = 15,037.75

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Why These Related Problems?

These problems maintain the same ratio (1.92) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.