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Finding the Third Proportional to 83 and 219

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Solution

The third proportional to 83 and 219 is: 577.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    83 : 219 = 219 : x
  2. Step 2: Convert to fraction form
    83/219 = 219/x
  3. Step 3: Cross multiply
    83x = 219 × 219
  4. Step 4: Simplify right side
    83x = 47,961
  5. Step 5: Solve for x
    x = 47,961/83
  6. Step 6: Final answer
    x = 577.84

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Why These Related Problems?

These problems maintain the same ratio (2.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.