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Finding the Third Proportional to 589 and 633

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Solution

The third proportional to 589 and 633 is: 680.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    589 : 633 = 633 : x
  2. Step 2: Convert to fraction form
    589/633 = 633/x
  3. Step 3: Cross multiply
    589x = 633 × 633
  4. Step 4: Simplify right side
    589x = 400,689
  5. Step 5: Solve for x
    x = 400,689/589
  6. Step 6: Final answer
    x = 680.29

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.