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Finding the Third Proportional to 121.78 and 284.20

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Solution

The third proportional to 121.78 and 284.20 is: 663.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    121.78 : 284.20 = 284.20 : x
  2. Step 2: Convert to fraction form
    121.78/284.20 = 284.20/x
  3. Step 3: Cross multiply
    121.78x = 284.20 × 284.20
  4. Step 4: Simplify right side
    121.78x = 80,771.42
  5. Step 5: Solve for x
    x = 80,771.42/121.78
  6. Step 6: Final answer
    x = 663.25

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.