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Finding the Third Proportional to 414,082 and 586,050

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Solution

The third proportional to 414,082 and 586,050 is: 829,436.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,082 : 586,050 = 586,050 : x
  2. Step 2: Convert to fraction form
    414,082/586,050 = 586,050/x
  3. Step 3: Cross multiply
    414,082x = 586,050 × 586,050
  4. Step 4: Simplify right side
    414,082x = 343,454,602,500
  5. Step 5: Solve for x
    x = 343,454,602,500/414,082
  6. Step 6: Final answer
    x = 829,436.20

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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.