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Finding the Third Proportional to 7,538 and 16,034

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Solution

The third proportional to 7,538 and 16,034 is: 34,105.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,538 : 16,034 = 16,034 : x
  2. Step 2: Convert to fraction form
    7,538/16,034 = 16,034/x
  3. Step 3: Cross multiply
    7,538x = 16,034 × 16,034
  4. Step 4: Simplify right side
    7,538x = 257,089,156
  5. Step 5: Solve for x
    x = 257,089,156/7,538
  6. Step 6: Final answer
    x = 34,105.75

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.