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Finding the Third Proportional to 2,142 and 2,203

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Solution

The third proportional to 2,142 and 2,203 is: 2,265.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,142 : 2,203 = 2,203 : x
  2. Step 2: Convert to fraction form
    2,142/2,203 = 2,203/x
  3. Step 3: Cross multiply
    2,142x = 2,203 × 2,203
  4. Step 4: Simplify right side
    2,142x = 4,853,209
  5. Step 5: Solve for x
    x = 4,853,209/2,142
  6. Step 6: Final answer
    x = 2,265.74

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Why These Related Problems?

These problems maintain the same ratio (1.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.