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Finding the Third Proportional to 180 and 431.75

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Solution

The third proportional to 180 and 431.75 is: 1,035.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    180 : 431.75 = 431.75 : x
  2. Step 2: Convert to fraction form
    180/431.75 = 431.75/x
  3. Step 3: Cross multiply
    180x = 431.75 × 431.75
  4. Step 4: Simplify right side
    180x = 186,408.06
  5. Step 5: Solve for x
    x = 186,408.06/180
  6. Step 6: Final answer
    x = 1,035.60

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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.