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Finding the Third Proportional to 82,296 and 177,066

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Solution

The third proportional to 82,296 and 177,066 is: 380,970.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,296 : 177,066 = 177,066 : x
  2. Step 2: Convert to fraction form
    82,296/177,066 = 177,066/x
  3. Step 3: Cross multiply
    82,296x = 177,066 × 177,066
  4. Step 4: Simplify right side
    82,296x = 31,352,368,356
  5. Step 5: Solve for x
    x = 31,352,368,356/82,296
  6. Step 6: Final answer
    x = 380,970.74

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.