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Finding the Third Proportional to 4,214 and 7,023

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Solution

The third proportional to 4,214 and 7,023 is: 11,704.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,214 : 7,023 = 7,023 : x
  2. Step 2: Convert to fraction form
    4,214/7,023 = 7,023/x
  3. Step 3: Cross multiply
    4,214x = 7,023 × 7,023
  4. Step 4: Simplify right side
    4,214x = 49,322,529
  5. Step 5: Solve for x
    x = 49,322,529/4,214
  6. Step 6: Final answer
    x = 11,704.44

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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.