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Finding the Third Proportional to 82,053 and 133,974

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Solution

The third proportional to 82,053 and 133,974 is: 218,749.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,053 : 133,974 = 133,974 : x
  2. Step 2: Convert to fraction form
    82,053/133,974 = 133,974/x
  3. Step 3: Cross multiply
    82,053x = 133,974 × 133,974
  4. Step 4: Simplify right side
    82,053x = 17,949,032,676
  5. Step 5: Solve for x
    x = 17,949,032,676/82,053
  6. Step 6: Final answer
    x = 218,749.26

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.