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Finding the Third Proportional to 589 and 646

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Solution

The third proportional to 589 and 646 is: 708.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    589 : 646 = 646 : x
  2. Step 2: Convert to fraction form
    589/646 = 646/x
  3. Step 3: Cross multiply
    589x = 646 × 646
  4. Step 4: Simplify right side
    589x = 417,316
  5. Step 5: Solve for x
    x = 417,316/589
  6. Step 6: Final answer
    x = 708.52

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.