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Finding the Third Proportional to 2,105 and 2,289

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Solution

The third proportional to 2,105 and 2,289 is: 2,489.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,105 : 2,289 = 2,289 : x
  2. Step 2: Convert to fraction form
    2,105/2,289 = 2,289/x
  3. Step 3: Cross multiply
    2,105x = 2,289 × 2,289
  4. Step 4: Simplify right side
    2,105x = 5,239,521
  5. Step 5: Solve for x
    x = 5,239,521/2,105
  6. Step 6: Final answer
    x = 2,489.08

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.