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Finding the Third Proportional to 9,675 and 19,106

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Solution

The third proportional to 9,675 and 19,106 is: 37,730.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,675 : 19,106 = 19,106 : x
  2. Step 2: Convert to fraction form
    9,675/19,106 = 19,106/x
  3. Step 3: Cross multiply
    9,675x = 19,106 × 19,106
  4. Step 4: Simplify right side
    9,675x = 365,039,236
  5. Step 5: Solve for x
    x = 365,039,236/9,675
  6. Step 6: Final answer
    x = 37,730.15

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.