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Finding the Third Proportional to 13,219 and 20,458

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Solution

The third proportional to 13,219 and 20,458 is: 31,661.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,219 : 20,458 = 20,458 : x
  2. Step 2: Convert to fraction form
    13,219/20,458 = 20,458/x
  3. Step 3: Cross multiply
    13,219x = 20,458 × 20,458
  4. Step 4: Simplify right side
    13,219x = 418,529,764
  5. Step 5: Solve for x
    x = 418,529,764/13,219
  6. Step 6: Final answer
    x = 31,661.23

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.