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Finding the Third Proportional to 416,678 and 589,984

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Solution

The third proportional to 416,678 and 589,984 is: 835,371.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    416,678 : 589,984 = 589,984 : x
  2. Step 2: Convert to fraction form
    416,678/589,984 = 589,984/x
  3. Step 3: Cross multiply
    416,678x = 589,984 × 589,984
  4. Step 4: Simplify right side
    416,678x = 348,081,120,256
  5. Step 5: Solve for x
    x = 348,081,120,256/416,678
  6. Step 6: Final answer
    x = 835,371.97

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.