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Finding the Third Proportional to 1,277 and 1,397

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Solution

The third proportional to 1,277 and 1,397 is: 1,528.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,277 : 1,397 = 1,397 : x
  2. Step 2: Convert to fraction form
    1,277/1,397 = 1,397/x
  3. Step 3: Cross multiply
    1,277x = 1,397 × 1,397
  4. Step 4: Simplify right side
    1,277x = 1,951,609
  5. Step 5: Solve for x
    x = 1,951,609/1,277
  6. Step 6: Final answer
    x = 1,528.28

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.