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Finding the Third Proportional to 7,698 and 10,077

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Solution

The third proportional to 7,698 and 10,077 is: 13,191.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,698 : 10,077 = 10,077 : x
  2. Step 2: Convert to fraction form
    7,698/10,077 = 10,077/x
  3. Step 3: Cross multiply
    7,698x = 10,077 × 10,077
  4. Step 4: Simplify right side
    7,698x = 101,545,929
  5. Step 5: Solve for x
    x = 101,545,929/7,698
  6. Step 6: Final answer
    x = 13,191.21

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.