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Finding the Third Proportional to 9,714 and 14,534

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Solution

The third proportional to 9,714 and 14,534 is: 21,745.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,714 : 14,534 = 14,534 : x
  2. Step 2: Convert to fraction form
    9,714/14,534 = 14,534/x
  3. Step 3: Cross multiply
    9,714x = 14,534 × 14,534
  4. Step 4: Simplify right side
    9,714x = 211,237,156
  5. Step 5: Solve for x
    x = 211,237,156/9,714
  6. Step 6: Final answer
    x = 21,745.64

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.