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Finding the Third Proportional to 419.25 and 589.31

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Solution

The third proportional to 419.25 and 589.31 is: 828.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.25 : 589.31 = 589.31 : x
  2. Step 2: Convert to fraction form
    419.25/589.31 = 589.31/x
  3. Step 3: Cross multiply
    419.25x = 589.31 × 589.31
  4. Step 4: Simplify right side
    419.25x = 347,289.22
  5. Step 5: Solve for x
    x = 347,289.22/419.25
  6. Step 6: Final answer
    x = 828.36

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.