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Finding the Third Proportional to 864 and 1,684

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Solution

The third proportional to 864 and 1,684 is: 3,282.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    864 : 1,684 = 1,684 : x
  2. Step 2: Convert to fraction form
    864/1,684 = 1,684/x
  3. Step 3: Cross multiply
    864x = 1,684 × 1,684
  4. Step 4: Simplify right side
    864x = 2,835,856
  5. Step 5: Solve for x
    x = 2,835,856/864
  6. Step 6: Final answer
    x = 3,282.24

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.