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Finding the Third Proportional to 728 and 1,286

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Solution

The third proportional to 728 and 1,286 is: 2,271.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    728 : 1,286 = 1,286 : x
  2. Step 2: Convert to fraction form
    728/1,286 = 1,286/x
  3. Step 3: Cross multiply
    728x = 1,286 × 1,286
  4. Step 4: Simplify right side
    728x = 1,653,796
  5. Step 5: Solve for x
    x = 1,653,796/728
  6. Step 6: Final answer
    x = 2,271.70

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.