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Finding the Third Proportional to 260,857 and 414,632

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Solution

The third proportional to 260,857 and 414,632 is: 659,057.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    260,857 : 414,632 = 414,632 : x
  2. Step 2: Convert to fraction form
    260,857/414,632 = 414,632/x
  3. Step 3: Cross multiply
    260,857x = 414,632 × 414,632
  4. Step 4: Simplify right side
    260,857x = 171,919,695,424
  5. Step 5: Solve for x
    x = 171,919,695,424/260,857
  6. Step 6: Final answer
    x = 659,057.24

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.