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Finding the Third Proportional to 966 and 1,462.25

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Solution

The third proportional to 966 and 1,462.25 is: 2,213.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    966 : 1,462.25 = 1,462.25 : x
  2. Step 2: Convert to fraction form
    966/1,462.25 = 1,462.25/x
  3. Step 3: Cross multiply
    966x = 1,462.25 × 1,462.25
  4. Step 4: Simplify right side
    966x = 2,138,175.06
  5. Step 5: Solve for x
    x = 2,138,175.06/966
  6. Step 6: Final answer
    x = 2,213.43

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.