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Finding the Third Proportional to 83,517 and 182,024

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Solution

The third proportional to 83,517 and 182,024 is: 396,718.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,517 : 182,024 = 182,024 : x
  2. Step 2: Convert to fraction form
    83,517/182,024 = 182,024/x
  3. Step 3: Cross multiply
    83,517x = 182,024 × 182,024
  4. Step 4: Simplify right side
    83,517x = 33,132,736,576
  5. Step 5: Solve for x
    x = 33,132,736,576/83,517
  6. Step 6: Final answer
    x = 396,718.47

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.