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Finding the Third Proportional to 164 and 258

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Solution

The third proportional to 164 and 258 is: 405.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    164 : 258 = 258 : x
  2. Step 2: Convert to fraction form
    164/258 = 258/x
  3. Step 3: Cross multiply
    164x = 258 × 258
  4. Step 4: Simplify right side
    164x = 66,564
  5. Step 5: Solve for x
    x = 66,564/164
  6. Step 6: Final answer
    x = 405.88

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.