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Finding the Third Proportional to 414,030 and 585,972

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Solution

The third proportional to 414,030 and 585,972 is: 829,319.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,030 : 585,972 = 585,972 : x
  2. Step 2: Convert to fraction form
    414,030/585,972 = 585,972/x
  3. Step 3: Cross multiply
    414,030x = 585,972 × 585,972
  4. Step 4: Simplify right side
    414,030x = 343,363,184,784
  5. Step 5: Solve for x
    x = 343,363,184,784/414,030
  6. Step 6: Final answer
    x = 829,319.58

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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.