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Finding the Third Proportional to 1,298 and 2,009

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Solution

The third proportional to 1,298 and 2,009 is: 3,109.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,298 : 2,009 = 2,009 : x
  2. Step 2: Convert to fraction form
    1,298/2,009 = 2,009/x
  3. Step 3: Cross multiply
    1,298x = 2,009 × 2,009
  4. Step 4: Simplify right side
    1,298x = 4,036,081
  5. Step 5: Solve for x
    x = 4,036,081/1,298
  6. Step 6: Final answer
    x = 3,109.46

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.