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Finding the Third Proportional to 414.70 and 589.36

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Solution

The third proportional to 414.70 and 589.36 is: 837.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.70 : 589.36 = 589.36 : x
  2. Step 2: Convert to fraction form
    414.70/589.36 = 589.36/x
  3. Step 3: Cross multiply
    414.70x = 589.36 × 589.36
  4. Step 4: Simplify right side
    414.70x = 347,344.47
  5. Step 5: Solve for x
    x = 347,344.47/414.70
  6. Step 6: Final answer
    x = 837.57

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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.