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Finding the Third Proportional to 2,099 and 4,174

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Solution

The third proportional to 2,099 and 4,174 is: 8,300.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,099 : 4,174 = 4,174 : x
  2. Step 2: Convert to fraction form
    2,099/4,174 = 4,174/x
  3. Step 3: Cross multiply
    2,099x = 4,174 × 4,174
  4. Step 4: Simplify right side
    2,099x = 17,422,276
  5. Step 5: Solve for x
    x = 17,422,276/2,099
  6. Step 6: Final answer
    x = 8,300.27

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Why These Related Problems?

These problems maintain the same ratio (1.99) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.