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Finding the Third Proportional to 1,684 and 3,646

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Solution

The third proportional to 1,684 and 3,646 is: 7,893.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,684 : 3,646 = 3,646 : x
  2. Step 2: Convert to fraction form
    1,684/3,646 = 3,646/x
  3. Step 3: Cross multiply
    1,684x = 3,646 × 3,646
  4. Step 4: Simplify right side
    1,684x = 13,293,316
  5. Step 5: Solve for x
    x = 13,293,316/1,684
  6. Step 6: Final answer
    x = 7,893.89

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.