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Finding the Third Proportional to 81,946 and 177,014

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Solution

The third proportional to 81,946 and 177,014 is: 382,373.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,946 : 177,014 = 177,014 : x
  2. Step 2: Convert to fraction form
    81,946/177,014 = 177,014/x
  3. Step 3: Cross multiply
    81,946x = 177,014 × 177,014
  4. Step 4: Simplify right side
    81,946x = 31,333,956,196
  5. Step 5: Solve for x
    x = 31,333,956,196/81,946
  6. Step 6: Final answer
    x = 382,373.22

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.