Question 581203
let d = daughter's present age
let f = father's present age
:
write an equation for each statement:
:
"A girl is now one-fourth as old as her father,
d = {{{1/4}}}f
or
f = 4d
:
"in seven years she will be one-half as old as her father was twelve years ago."
d + 7 = {{{1/2}}}(f-12)
multiply both sides by 2
2(d+7) = f - 12
2d + 14 = f - 12
2d = f - 12 - 14
2d = f - 26
From the 1st statement, replace f with 4d
2d = 4d - 26
26 = 4d - 2d 
26 = 2d
d = 13 yrs is daughter's age
then
4(13) = 52 yrs is father's present age
;
;
Check this in the statement:
"in seven years she will be one-half as old as her father was twelve years ago."
13 + 7 = {{{1/2}}}(52-12)
20 = {{{1/2}}}(40)