Question 150366: If leah is 6 years older than her sister,Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is sue?
Found 2 solutions by vleith, Earlsdon:
Answer by vleith(2983)   (Show Source):
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! Let L = Leah's age, S = Sue's age, and J = John's age, then, from the problem description, you can write:
1) L = S+6 "Leah (L) is 6 years older (+) than Sue (S)".
2) J = L+5 "John (J) is 5 years older (+) than Leah (L)".
3) L+S+J = 41 "The total (sum) of their ages is 41 years.
So you now have a system of three equations with three unknowns (L, S, and J).
You can solve this system of equations by first eliminating one of the variables to leave you with two equations with two unknowns, then eliminate another variable to leave you with one equation with one unknown.
Here's how it works:
Start with:
L+S+J = 41 Substitute L = S+6 (Equation 1) to get:
(S+6)+S+J = 41 Now substitute J = L+5 (equation 2) to get:
(S+5)+S+(L+5) = 41 But, since you want to find Sue's (S) age, replace the L here with L = S+6 (equation 1) to leave you with:
(S+6)+S+((S+6)+5) = 41 Now you have one equation with one unknown (S) which you can easily solve by combining like-terms:
3S+17 = 41 Subtract 17 from both sides of the equation,
3S = 24 Finally, divide both sides by 3 to leave you with:
S = 8
So Sue is 8 years old.
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