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Finding the Third Proportional to 2,140 and 2,449

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Solution

The third proportional to 2,140 and 2,449 is: 2,802.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,140 : 2,449 = 2,449 : x
  2. Step 2: Convert to fraction form
    2,140/2,449 = 2,449/x
  3. Step 3: Cross multiply
    2,140x = 2,449 × 2,449
  4. Step 4: Simplify right side
    2,140x = 5,997,601
  5. Step 5: Solve for x
    x = 5,997,601/2,140
  6. Step 6: Final answer
    x = 2,802.62

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.