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Finding the Third Proportional to 2,099 and 2,963

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Solution

The third proportional to 2,099 and 2,963 is: 4,182.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,099 : 2,963 = 2,963 : x
  2. Step 2: Convert to fraction form
    2,099/2,963 = 2,963/x
  3. Step 3: Cross multiply
    2,099x = 2,963 × 2,963
  4. Step 4: Simplify right side
    2,099x = 8,779,369
  5. Step 5: Solve for x
    x = 8,779,369/2,099
  6. Step 6: Final answer
    x = 4,182.64

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.