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Finding the Third Proportional to 7,707 and 13,503

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Solution

The third proportional to 7,707 and 13,503 is: 23,657.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,707 : 13,503 = 13,503 : x
  2. Step 2: Convert to fraction form
    7,707/13,503 = 13,503/x
  3. Step 3: Cross multiply
    7,707x = 13,503 × 13,503
  4. Step 4: Simplify right side
    7,707x = 182,331,009
  5. Step 5: Solve for x
    x = 182,331,009/7,707
  6. Step 6: Final answer
    x = 23,657.84

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Why These Related Problems?

These problems maintain the same ratio (1.75) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.