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Finding the Third Proportional to 3,214 and 3,706

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Solution

The third proportional to 3,214 and 3,706 is: 4,273.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,214 : 3,706 = 3,706 : x
  2. Step 2: Convert to fraction form
    3,214/3,706 = 3,706/x
  3. Step 3: Cross multiply
    3,214x = 3,706 × 3,706
  4. Step 4: Simplify right side
    3,214x = 13,734,436
  5. Step 5: Solve for x
    x = 13,734,436/3,214
  6. Step 6: Final answer
    x = 4,273.32

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.