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Finding the Third Proportional to 4,210 and 6,589

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Solution

The third proportional to 4,210 and 6,589 is: 10,312.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,210 : 6,589 = 6,589 : x
  2. Step 2: Convert to fraction form
    4,210/6,589 = 6,589/x
  3. Step 3: Cross multiply
    4,210x = 6,589 × 6,589
  4. Step 4: Simplify right side
    4,210x = 43,414,921
  5. Step 5: Solve for x
    x = 43,414,921/4,210
  6. Step 6: Final answer
    x = 10,312.33

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.