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Finding the Third Proportional to 258.19 and 420.19

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Solution

The third proportional to 258.19 and 420.19 is: 683.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    258.19 : 420.19 = 420.19 : x
  2. Step 2: Convert to fraction form
    258.19/420.19 = 420.19/x
  3. Step 3: Cross multiply
    258.19x = 420.19 × 420.19
  4. Step 4: Simplify right side
    258.19x = 176,557.54
  5. Step 5: Solve for x
    x = 176,557.54/258.19
  6. Step 6: Final answer
    x = 683.83

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.