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Finding the Third Proportional to 829 and 1,215

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Solution

The third proportional to 829 and 1,215 is: 1,780.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,215 = 1,215 : x
  2. Step 2: Convert to fraction form
    829/1,215 = 1,215/x
  3. Step 3: Cross multiply
    829x = 1,215 × 1,215
  4. Step 4: Simplify right side
    829x = 1,476,225
  5. Step 5: Solve for x
    x = 1,476,225/829
  6. Step 6: Final answer
    x = 1,780.73

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.