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Finding the Third Proportional to 465 and 697

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Solution

The third proportional to 465 and 697 is: 1,044.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    465 : 697 = 697 : x
  2. Step 2: Convert to fraction form
    465/697 = 697/x
  3. Step 3: Cross multiply
    465x = 697 × 697
  4. Step 4: Simplify right side
    465x = 485,809
  5. Step 5: Solve for x
    x = 485,809/465
  6. Step 6: Final answer
    x = 1,044.75

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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.