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Finding the Third Proportional to 4,211 and 10,213

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Solution

The third proportional to 4,211 and 10,213 is: 24,769.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,211 : 10,213 = 10,213 : x
  2. Step 2: Convert to fraction form
    4,211/10,213 = 10,213/x
  3. Step 3: Cross multiply
    4,211x = 10,213 × 10,213
  4. Step 4: Simplify right side
    4,211x = 104,305,369
  5. Step 5: Solve for x
    x = 104,305,369/4,211
  6. Step 6: Final answer
    x = 24,769.74

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.