Question 1140064
 Amy is one third the age of her mother.
a = {{{1/3}}}m
or multiply equation by 3
m = 3a
In 12 years time, Amy will be half the age of her mother.
a + 12 = {{{1/2}}}(m+12)
a + 12 = {{{1/2}}}m + 6
a = {{{1/2}}}m + 6 - 12
a = {{{1/2}}}m - 6
get rid of the fraction, multiply by 2
2a = m - 12
replace m with 3a (from the 1st statement)
2a = 3a - 12
12 = 3a - 2a
a = 12 yrs is Amy's age
:
How old is Amy’s mother? 
3*12 = 36 yrs is Mom's age
:
:
See if that checks out in the statement
"In 12 years time, Amy will be half the age of her mother."
12 + 12 = {{{1/2}}}(36 + 12)
24 = {{{1/2}}}* 48