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Finding the Third Proportional to 4,210 and 9,682

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Solution

The third proportional to 4,210 and 9,682 is: 22,266.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,210 : 9,682 = 9,682 : x
  2. Step 2: Convert to fraction form
    4,210/9,682 = 9,682/x
  3. Step 3: Cross multiply
    4,210x = 9,682 × 9,682
  4. Step 4: Simplify right side
    4,210x = 93,741,124
  5. Step 5: Solve for x
    x = 93,741,124/4,210
  6. Step 6: Final answer
    x = 22,266.30

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.