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Finding the Third Proportional to 7,684 and 19,114

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Solution

The third proportional to 7,684 and 19,114 is: 47,546.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,684 : 19,114 = 19,114 : x
  2. Step 2: Convert to fraction form
    7,684/19,114 = 19,114/x
  3. Step 3: Cross multiply
    7,684x = 19,114 × 19,114
  4. Step 4: Simplify right side
    7,684x = 365,344,996
  5. Step 5: Solve for x
    x = 365,344,996/7,684
  6. Step 6: Final answer
    x = 47,546.20

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Why These Related Problems?

These problems maintain the same ratio (2.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.