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Finding the Third Proportional to 829 and 1,329

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Solution

The third proportional to 829 and 1,329 is: 2,130.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,329 = 1,329 : x
  2. Step 2: Convert to fraction form
    829/1,329 = 1,329/x
  3. Step 3: Cross multiply
    829x = 1,329 × 1,329
  4. Step 4: Simplify right side
    829x = 1,766,241
  5. Step 5: Solve for x
    x = 1,766,241/829
  6. Step 6: Final answer
    x = 2,130.57

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.