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Finding the Third Proportional to 2,049 and 4,170

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Solution

The third proportional to 2,049 and 4,170 is: 8,486.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,049 : 4,170 = 4,170 : x
  2. Step 2: Convert to fraction form
    2,049/4,170 = 4,170/x
  3. Step 3: Cross multiply
    2,049x = 4,170 × 4,170
  4. Step 4: Simplify right side
    2,049x = 17,388,900
  5. Step 5: Solve for x
    x = 17,388,900/2,049
  6. Step 6: Final answer
    x = 8,486.53

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.