SOLUTION: this year, jake is 5 years older than his sister. three years ago, jake was twice his sisters age. How old is each person now?

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Question 1135944: this year, jake is 5 years older than his sister. three years ago, jake was twice his sisters age. How old is each person now?

Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
x+5 and x, Jake and sister

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Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let j = jakes' age.
let s = his sister's age.

this year, jake is 5 years older than his sister.

j = s + 5

three years ago, jake was twice his sister's age.

j - 3 = 2 * (s - 3)

simplify to get j - 3 = 2s - 6

add 3 to both sides of the equation to get j = 2s - 3

since j = s + 5, replace j with s + 5 in this latest equation to get:

s + 5 = 2s - 3

subract s from both sides of this equaiton and add 3 to both sides of this equation to get:

8 = s.

his sister is 8 years old today.
jake is 13 years old today.

3 years ago jake was 10 and his sister was 5 which made jake 2 times his sister's age.

solution looks good.

solution is jake is 13 and his sister is 8 now.