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Finding the Third Proportional to 9,700 and 14,509

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Solution

The third proportional to 9,700 and 14,509 is: 21,702.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,700 : 14,509 = 14,509 : x
  2. Step 2: Convert to fraction form
    9,700/14,509 = 14,509/x
  3. Step 3: Cross multiply
    9,700x = 14,509 × 14,509
  4. Step 4: Simplify right side
    9,700x = 210,511,081
  5. Step 5: Solve for x
    x = 210,511,081/9,700
  6. Step 6: Final answer
    x = 21,702.17

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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.