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Finding the Third Proportional to 301 and 419.75

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Solution

The third proportional to 301 and 419.75 is: 585.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    301 : 419.75 = 419.75 : x
  2. Step 2: Convert to fraction form
    301/419.75 = 419.75/x
  3. Step 3: Cross multiply
    301x = 419.75 × 419.75
  4. Step 4: Simplify right side
    301x = 176,190.06
  5. Step 5: Solve for x
    x = 176,190.06/301
  6. Step 6: Final answer
    x = 585.35

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.