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Finding the Third Proportional to 2,106 and 4,509

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Solution

The third proportional to 2,106 and 4,509 is: 9,653.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,106 : 4,509 = 4,509 : x
  2. Step 2: Convert to fraction form
    2,106/4,509 = 4,509/x
  3. Step 3: Cross multiply
    2,106x = 4,509 × 4,509
  4. Step 4: Simplify right side
    2,106x = 20,331,081
  5. Step 5: Solve for x
    x = 20,331,081/2,106
  6. Step 6: Final answer
    x = 9,653.88

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.