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Finding the Third Proportional to 224 and 323

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Solution

The third proportional to 224 and 323 is: 465.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    224 : 323 = 323 : x
  2. Step 2: Convert to fraction form
    224/323 = 323/x
  3. Step 3: Cross multiply
    224x = 323 × 323
  4. Step 4: Simplify right side
    224x = 104,329
  5. Step 5: Solve for x
    x = 104,329/224
  6. Step 6: Final answer
    x = 465.75

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.