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Finding the Third Proportional to 75 and 177.38

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Solution

The third proportional to 75 and 177.38 is: 419.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    75 : 177.38 = 177.38 : x
  2. Step 2: Convert to fraction form
    75/177.38 = 177.38/x
  3. Step 3: Cross multiply
    75x = 177.38 × 177.38
  4. Step 4: Simplify right side
    75x = 31,461.89
  5. Step 5: Solve for x
    x = 31,461.89/75
  6. Step 6: Final answer
    x = 419.49

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.