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Finding the Third Proportional to 829 and 1,837

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Solution

The third proportional to 829 and 1,837 is: 4,070.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,837 = 1,837 : x
  2. Step 2: Convert to fraction form
    829/1,837 = 1,837/x
  3. Step 3: Cross multiply
    829x = 1,837 × 1,837
  4. Step 4: Simplify right side
    829x = 3,374,569
  5. Step 5: Solve for x
    x = 3,374,569/829
  6. Step 6: Final answer
    x = 4,070.65

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.