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Finding the Third Proportional to 466 and 691

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Solution

The third proportional to 466 and 691 is: 1,024.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    466 : 691 = 691 : x
  2. Step 2: Convert to fraction form
    466/691 = 691/x
  3. Step 3: Cross multiply
    466x = 691 × 691
  4. Step 4: Simplify right side
    466x = 477,481
  5. Step 5: Solve for x
    x = 477,481/466
  6. Step 6: Final answer
    x = 1,024.64

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.