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Finding the Third Proportional to 1,947 and 2,109

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Solution

The third proportional to 1,947 and 2,109 is: 2,284.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,947 : 2,109 = 2,109 : x
  2. Step 2: Convert to fraction form
    1,947/2,109 = 2,109/x
  3. Step 3: Cross multiply
    1,947x = 2,109 × 2,109
  4. Step 4: Simplify right side
    1,947x = 4,447,881
  5. Step 5: Solve for x
    x = 4,447,881/1,947
  6. Step 6: Final answer
    x = 2,284.48

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.