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Finding the Third Proportional to 649 and 971

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Solution

The third proportional to 649 and 971 is: 1,452.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    649 : 971 = 971 : x
  2. Step 2: Convert to fraction form
    649/971 = 971/x
  3. Step 3: Cross multiply
    649x = 971 × 971
  4. Step 4: Simplify right side
    649x = 942,841
  5. Step 5: Solve for x
    x = 942,841/649
  6. Step 6: Final answer
    x = 1,452.76

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.