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Finding the Third Proportional to 82,434 and 177,668

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Solution

The third proportional to 82,434 and 177,668 is: 382,923.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,434 : 177,668 = 177,668 : x
  2. Step 2: Convert to fraction form
    82,434/177,668 = 177,668/x
  3. Step 3: Cross multiply
    82,434x = 177,668 × 177,668
  4. Step 4: Simplify right side
    82,434x = 31,565,918,224
  5. Step 5: Solve for x
    x = 31,565,918,224/82,434
  6. Step 6: Final answer
    x = 382,923.53

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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.