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Finding the Third Proportional to 1,297 and 1,897

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Solution

The third proportional to 1,297 and 1,897 is: 2,774.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,297 : 1,897 = 1,897 : x
  2. Step 2: Convert to fraction form
    1,297/1,897 = 1,897/x
  3. Step 3: Cross multiply
    1,297x = 1,897 × 1,897
  4. Step 4: Simplify right side
    1,297x = 3,598,609
  5. Step 5: Solve for x
    x = 3,598,609/1,297
  6. Step 6: Final answer
    x = 2,774.56

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These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.