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Finding the Third Proportional to 243 and 402.25

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Solution

The third proportional to 243 and 402.25 is: 665.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    243 : 402.25 = 402.25 : x
  2. Step 2: Convert to fraction form
    243/402.25 = 402.25/x
  3. Step 3: Cross multiply
    243x = 402.25 × 402.25
  4. Step 4: Simplify right side
    243x = 161,805.06
  5. Step 5: Solve for x
    x = 161,805.06/243
  6. Step 6: Final answer
    x = 665.86

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.