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Finding the Third Proportional to 83,054 and 194,982

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Solution

The third proportional to 83,054 and 194,982 is: 457,750.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,054 : 194,982 = 194,982 : x
  2. Step 2: Convert to fraction form
    83,054/194,982 = 194,982/x
  3. Step 3: Cross multiply
    83,054x = 194,982 × 194,982
  4. Step 4: Simplify right side
    83,054x = 38,017,980,324
  5. Step 5: Solve for x
    x = 38,017,980,324/83,054
  6. Step 6: Final answer
    x = 457,750.14

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.