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Finding the Third Proportional to 224 and 491

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Solution

The third proportional to 224 and 491 is: 1,076.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    224 : 491 = 491 : x
  2. Step 2: Convert to fraction form
    224/491 = 491/x
  3. Step 3: Cross multiply
    224x = 491 × 491
  4. Step 4: Simplify right side
    224x = 241,081
  5. Step 5: Solve for x
    x = 241,081/224
  6. Step 6: Final answer
    x = 1,076.25

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.