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Finding the Third Proportional to 829 and 1,658

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Solution

The third proportional to 829 and 1,658 is: 3,316

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,658 = 1,658 : x
  2. Step 2: Convert to fraction form
    829/1,658 = 1,658/x
  3. Step 3: Cross multiply
    829x = 1,658 × 1,658
  4. Step 4: Simplify right side
    829x = 2,748,964
  5. Step 5: Solve for x
    x = 2,748,964/829
  6. Step 6: Final answer
    x = 3,316

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Why These Related Problems?

These problems maintain the same ratio (2) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.