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Finding the Third Proportional to 232.25 and 589.75

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Solution

The third proportional to 232.25 and 589.75 is: 1,497.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    232.25 : 589.75 = 589.75 : x
  2. Step 2: Convert to fraction form
    232.25/589.75 = 589.75/x
  3. Step 3: Cross multiply
    232.25x = 589.75 × 589.75
  4. Step 4: Simplify right side
    232.25x = 347,805.06
  5. Step 5: Solve for x
    x = 347,805.06/232.25
  6. Step 6: Final answer
    x = 1,497.55

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Why These Related Problems?

These problems maintain the same ratio (2.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.