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Finding the Third Proportional to 2,099 and 4,597

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Solution

The third proportional to 2,099 and 4,597 is: 10,067.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,099 : 4,597 = 4,597 : x
  2. Step 2: Convert to fraction form
    2,099/4,597 = 4,597/x
  3. Step 3: Cross multiply
    2,099x = 4,597 × 4,597
  4. Step 4: Simplify right side
    2,099x = 21,132,409
  5. Step 5: Solve for x
    x = 21,132,409/2,099
  6. Step 6: Final answer
    x = 10,067.85

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.