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Finding the Third Proportional to 2,089 and 3,142

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Solution

The third proportional to 2,089 and 3,142 is: 4,725.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,089 : 3,142 = 3,142 : x
  2. Step 2: Convert to fraction form
    2,089/3,142 = 3,142/x
  3. Step 3: Cross multiply
    2,089x = 3,142 × 3,142
  4. Step 4: Simplify right side
    2,089x = 9,872,164
  5. Step 5: Solve for x
    x = 9,872,164/2,089
  6. Step 6: Final answer
    x = 4,725.78

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.