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Finding the Third Proportional to 82 and 178

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Solution

The third proportional to 82 and 178 is: 386.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    82 : 178 = 178 : x
  2. Step 2: Convert to fraction form
    82/178 = 178/x
  3. Step 3: Cross multiply
    82x = 178 × 178
  4. Step 4: Simplify right side
    82x = 31,684
  5. Step 5: Solve for x
    x = 31,684/82
  6. Step 6: Final answer
    x = 386.39

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.