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Finding the Third Proportional to 420.19 and 649.69

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Solution

The third proportional to 420.19 and 649.69 is: 1,004.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.19 : 649.69 = 649.69 : x
  2. Step 2: Convert to fraction form
    420.19/649.69 = 649.69/x
  3. Step 3: Cross multiply
    420.19x = 649.69 × 649.69
  4. Step 4: Simplify right side
    420.19x = 422,093.85
  5. Step 5: Solve for x
    x = 422,093.85/420.19
  6. Step 6: Final answer
    x = 1,004.54

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.