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Finding the Third Proportional to 281,036 and 414,109

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Solution

The third proportional to 281,036 and 414,109 is: 610,193.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    281,036 : 414,109 = 414,109 : x
  2. Step 2: Convert to fraction form
    281,036/414,109 = 414,109/x
  3. Step 3: Cross multiply
    281,036x = 414,109 × 414,109
  4. Step 4: Simplify right side
    281,036x = 171,486,263,881
  5. Step 5: Solve for x
    x = 171,486,263,881/281,036
  6. Step 6: Final answer
    x = 610,193.23

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.