Answer: choice A) 8
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Work Shown:
L = Leah's age, S = Sue's age, J = John's age
"Leah is 6 years older than Sue" ----> L = S+6
"John is 5 years older than Leah" ----> J = L+5
"total of their ages is 41" ---> L+S+J = 41
Let's use substitution to get an equation with only one variable.
L+S+J = 41
L+S+L+5 = 41 ... replace J with L+5 (works since J = L+5)
2L+S+5 = 41
2(S+6)+S+5 = 41 ... replace L with S+6. Now we have only one variable
2S+12+S+5 = 41
3S+17 = 41
3S+17-17 = 41-17 ... subtract 17 from both sides
3S = 24
3S/3 = 24/3 ... divide both sides by 3
S = 8
Therefore Sue is 8 years old which is the answer we want.
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At this point we can stop, but as a bonus, let's find the other ages.
We can use Sue's age to find Leah's age
L = S+6
L = 8+6 ... replace S with 8
L = 14
Then use this age to find how old John is
J = L+5
J = 14+5 ... replace L with 14
J = 19
So Sue is 8, Leah is 14, John is 19. Adding up their ages gets us: 8+14+19 = 41 which confirms the right answer.