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Finding the Third Proportional to 174.75 and 419.81

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Solution

The third proportional to 174.75 and 419.81 is: 1,008.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    174.75 : 419.81 = 419.81 : x
  2. Step 2: Convert to fraction form
    174.75/419.81 = 419.81/x
  3. Step 3: Cross multiply
    174.75x = 419.81 × 419.81
  4. Step 4: Simplify right side
    174.75x = 176,242.54
  5. Step 5: Solve for x
    x = 176,242.54/174.75
  6. Step 6: Final answer
    x = 1,008.54

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.