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Finding the Third Proportional to 974 and 2,009

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Solution

The third proportional to 974 and 2,009 is: 4,143.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    974 : 2,009 = 2,009 : x
  2. Step 2: Convert to fraction form
    974/2,009 = 2,009/x
  3. Step 3: Cross multiply
    974x = 2,009 × 2,009
  4. Step 4: Simplify right side
    974x = 4,036,081
  5. Step 5: Solve for x
    x = 4,036,081/974
  6. Step 6: Final answer
    x = 4,143.82

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.