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Finding the Third Proportional to 3,414 and 4,023

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Solution

The third proportional to 3,414 and 4,023 is: 4,740.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,414 : 4,023 = 4,023 : x
  2. Step 2: Convert to fraction form
    3,414/4,023 = 4,023/x
  3. Step 3: Cross multiply
    3,414x = 4,023 × 4,023
  4. Step 4: Simplify right side
    3,414x = 16,184,529
  5. Step 5: Solve for x
    x = 16,184,529/3,414
  6. Step 6: Final answer
    x = 4,740.64

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.