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Finding the Third Proportional to 174 and 419.75

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Solution

The third proportional to 174 and 419.75 is: 1,012.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    174 : 419.75 = 419.75 : x
  2. Step 2: Convert to fraction form
    174/419.75 = 419.75/x
  3. Step 3: Cross multiply
    174x = 419.75 × 419.75
  4. Step 4: Simplify right side
    174x = 176,190.06
  5. Step 5: Solve for x
    x = 176,190.06/174
  6. Step 6: Final answer
    x = 1,012.59

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.