If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41, then how old is Sue?

Let the age of each person be represented by the initial letter of their name.

L = S + 6 ...(1)

J = S + 11 ...(2)

J + S + L = 41  ...(3)

From (3)

L = 41 - S - J

substitute for L in (1)

41 -S -J = S + 6

simplify

35 -J = 2S

S = (35 - J)/2

sub in (2)

J = (35 - J)/2 + 11

Multiply both sides by 2

2J = 35 -J +22

3J = 57

J is aged 19

Therefore S is aged 8

Therefore L is aged 14

J + S + L = 41 - answer checks.