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Finding the Third Proportional to 196.75 and 289.75

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Solution

The third proportional to 196.75 and 289.75 is: 426.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    196.75 : 289.75 = 289.75 : x
  2. Step 2: Convert to fraction form
    196.75/289.75 = 289.75/x
  3. Step 3: Cross multiply
    196.75x = 289.75 × 289.75
  4. Step 4: Simplify right side
    196.75x = 83,955.06
  5. Step 5: Solve for x
    x = 83,955.06/196.75
  6. Step 6: Final answer
    x = 426.71

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.