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Finding the Third Proportional to 3,205 and 5,780

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Solution

The third proportional to 3,205 and 5,780 is: 10,423.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,205 : 5,780 = 5,780 : x
  2. Step 2: Convert to fraction form
    3,205/5,780 = 5,780/x
  3. Step 3: Cross multiply
    3,205x = 5,780 × 5,780
  4. Step 4: Simplify right side
    3,205x = 33,408,400
  5. Step 5: Solve for x
    x = 33,408,400/3,205
  6. Step 6: Final answer
    x = 10,423.84

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Why These Related Problems?

These problems maintain the same ratio (1.80) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.