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Finding the Third Proportional to 589 and 1,230

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Solution

The third proportional to 589 and 1,230 is: 2,568.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    589 : 1,230 = 1,230 : x
  2. Step 2: Convert to fraction form
    589/1,230 = 1,230/x
  3. Step 3: Cross multiply
    589x = 1,230 × 1,230
  4. Step 4: Simplify right side
    589x = 1,512,900
  5. Step 5: Solve for x
    x = 1,512,900/589
  6. Step 6: Final answer
    x = 2,568.59

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.