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Finding the Third Proportional to 2,297 and 3,514

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Solution

The third proportional to 2,297 and 3,514 is: 5,375.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,297 : 3,514 = 3,514 : x
  2. Step 2: Convert to fraction form
    2,297/3,514 = 3,514/x
  3. Step 3: Cross multiply
    2,297x = 3,514 × 3,514
  4. Step 4: Simplify right side
    2,297x = 12,348,196
  5. Step 5: Solve for x
    x = 12,348,196/2,297
  6. Step 6: Final answer
    x = 5,375.79

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.