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Finding the Third Proportional to 189,384 and 414,407

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Solution

The third proportional to 189,384 and 414,407 is: 906,798.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    189,384 : 414,407 = 414,407 : x
  2. Step 2: Convert to fraction form
    189,384/414,407 = 414,407/x
  3. Step 3: Cross multiply
    189,384x = 414,407 × 414,407
  4. Step 4: Simplify right side
    189,384x = 171,733,161,649
  5. Step 5: Solve for x
    x = 171,733,161,649/189,384
  6. Step 6: Final answer
    x = 906,798.68

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.