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

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

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