Claire’s mother is 4 years more than twice Claire’s age. The sum of their ages is 58 years. 

• choixongdong: Let x = Claire's age
  Claire’s mother is 4 years more than twice Claire’s age = 2x + 4
  The sum of their ages is 58 years:
  x + 2x + 4 = 58
  3x + 4 = 58
  3x = 54
  x = 18
  
  Claire's age = 18
  Claire’s mother = 2(18)+4 = 36 + 4 = 40
  
• musiclover10045: claire's age = x
  
  claire's mothers age = 2x+4 ( 4 more than twice claire's age)
  
  sum is addition
  
  x + 2x+4 = 58
  
  add like terms ( x +2x = 3x)
  
  3x +4 = 58
  
  subtract 4 from each side:
  
  3x = 54
  
  divide both sides by 3
  x = 54 /3
  x = 18
  
  Claire is 18 years old
   Claire's mother is  2*18 = 36 +4 = 40 years old