SOLUTION: what is the answer to this word problem? Lisa noticed that in 7 years she'll be half her mother's age. If 3 years ago Lisa wa s 1/3 her mother's age, how old is her mother now?

Question 890222: what is the answer to this word problem? Lisa noticed that in 7 years she'll be half her mother's age. If 3 years ago Lisa wa s 1/3 her mother's age, how old is her mother now?
Found 2 solutions by ankor@dixie-net.com, rothauserc:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let L = Lisa's present age
let M = mother's present age
:
Write an equation for each statement:
:
" Lisa noticed that in 7 years she'll be half her mother's age."
L + 7 = (M+7)
multiply both sides by 2
2(L+7) = M + 7
2L + 14 = M + 7
2L + 14 - 7 = M
M = (2L+7)
:
" If 3 years ago Lisa wa s 1/3 her mother's age,"
L - 3 = (M-3)
multiply for sides by 3
3(L-3) = M - 3
3L - 9 = M - 3
3L = M - 3 + 9
3L = M + 6
Replace M with (2L+7) from the 1st statement
3L = 2L+7 + 6
3L = 2L + 13
3L - 2L = 13
L = 13 yrs is Lisa's age
;
how old is her mother now?
M = 2L + 7
M = 2(13) + 7
M = 33 yr's Mom's age
;
:
You can confirm these solutions by using these values in both statements
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be lisa's age and y be her mother's age, then
x +7 = y /2
x -3 = y /3
solve the first equation for x
first multiply both sides of = by 2
2x +14 = y
2x = y -14
x = y/2 -7
substitute for x in second equation
y/2 -7 -3 = y / 3
multiply both sides of = by 6
3y -60 = 2y
y = 60
Lisa's mother is 60 years old

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