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Finding the Third Proportional to 289.69 and 420.38

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Solution

The third proportional to 289.69 and 420.38 is: 610.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    289.69 : 420.38 = 420.38 : x
  2. Step 2: Convert to fraction form
    289.69/420.38 = 420.38/x
  3. Step 3: Cross multiply
    289.69x = 420.38 × 420.38
  4. Step 4: Simplify right side
    289.69x = 176,715.14
  5. Step 5: Solve for x
    x = 176,715.14/289.69
  6. Step 6: Final answer
    x = 610.02

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.