Question 471286
Milly is two thirds as old as Marcia.
 Four years from now she will be at most five sevenths as old as Marcia.
 At least how old is Milly?
:
let mi = Milly's present age
let ma = Marcia's present age
:
Write an equation for each statement:
:
"Milly is two thirds as old as Marcia."
mi = {{{2/3}}}ma
:
" Four years from now she will be at most five sevenths as old as Marcia. 
mi + 4 =< {{{5/7}}}(ma+4)
multiply both sides by 7
7(mi+4) =< 5(ma+4)
7mi + 28 =< 5ma + 20
7mi =< 5ma + 20 - 28
7mi =< 5ma - 8
Replace mi with {{{2/3}}}ma
7({{{2/3}}}ma) =< 5ma - 8
multiply both sides by 3
14ma =< 15ma - 24
14 ma - 15ma =< - 24 
-1ma =< -24
multiply both sides by -1, this reverses the inequality sign
ma => 24
then
mi => {{{2/3}}}*24 
mi => 16