Leah is 6 years older than Sue, John is 5 years older than Leah. Total combined age is 41. How old is Sue?

Sue's age (S) is Leah's age minus 6 (L - 6), so S = L - 6.

John's Age (J) is 5 + Lea's age (L), so J = L + 5

Leah (L) is Sue's age + 6, or L = S + 6

Since their total combined age is 41, then Sue's age + John's age + Leah's age = 41, or

L - 6 + L + 5 + S + 6 = 41. Combine the L's and the numbers to get 2L + 5 + S = 41. Since S = L - 6, you can substitute "L - 6" for "S" to eliminate a variable, which would give you 2L + 5 + L - 6 = 41. Combine the L's and numbers again and you get 3L - 1 = 41. Add 1 to both sides to clear the one on the left: 3L - 1 + 1 = 41 + 1, or 3L = 42. Divide both sides by 3 to find L: 3L/3 = 42/3. L = 14. CHECK - does 14 x 3 = 42? If it does, you're doing great. If not you made a mistake somewhere and should start by redoing the division, then working backwards from there, if necessary.

Since L = 14, then Leah is 14 years old. To find S and J, you simply substitute: S (Sue's age) = L - 6 = 14 - 6 = 8. J (John's age) = L + 5 = 14 + 5 = 19, so Leah is 14, Sue is 8, and John is 19. CHECK - add 14 + 8 + 19. It has to equal 41, their combined ages. 14 + 8 = 22. 22 + 19 = 41. You did it right! If those numbers do NOT add up to 41, double check your addition, then work backwards from there, if necessary.

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