Question 890222
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 = {{{1/2}}}(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 = {{{1/3}}}(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