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Finding the Third Proportional to 414,079 and 586,045.50

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Solution

The third proportional to 414,079 and 586,045.50 is: 829,429.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,079 : 586,045.50 = 586,045.50 : x
  2. Step 2: Convert to fraction form
    414,079/586,045.50 = 586,045.50/x
  3. Step 3: Cross multiply
    414,079x = 586,045.50 × 586,045.50
  4. Step 4: Simplify right side
    414,079x = 343,449,328,070.25
  5. Step 5: Solve for x
    x = 343,449,328,070.25/414,079
  6. Step 6: Final answer
    x = 829,429.48

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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.