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Finding the Third Proportional to 2,214 and 3,689

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Solution

The third proportional to 2,214 and 3,689 is: 6,146.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,214 : 3,689 = 3,689 : x
  2. Step 2: Convert to fraction form
    2,214/3,689 = 3,689/x
  3. Step 3: Cross multiply
    2,214x = 3,689 × 3,689
  4. Step 4: Simplify right side
    2,214x = 13,608,721
  5. Step 5: Solve for x
    x = 13,608,721/2,214
  6. Step 6: Final answer
    x = 6,146.67

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.