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Finding the Third Proportional to 9,854 and 14,034

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Solution

The third proportional to 9,854 and 14,034 is: 19,987.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,854 : 14,034 = 14,034 : x
  2. Step 2: Convert to fraction form
    9,854/14,034 = 14,034/x
  3. Step 3: Cross multiply
    9,854x = 14,034 × 14,034
  4. Step 4: Simplify right side
    9,854x = 196,953,156
  5. Step 5: Solve for x
    x = 196,953,156/9,854
  6. Step 6: Final answer
    x = 19,987.13

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.