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Finding the Third Proportional to 420.75 and 588.09

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Solution

The third proportional to 420.75 and 588.09 is: 821.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.75 : 588.09 = 588.09 : x
  2. Step 2: Convert to fraction form
    420.75/588.09 = 588.09/x
  3. Step 3: Cross multiply
    420.75x = 588.09 × 588.09
  4. Step 4: Simplify right side
    420.75x = 345,854.26
  5. Step 5: Solve for x
    x = 345,854.26/420.75
  6. Step 6: Final answer
    x = 821.99

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.