SOLUTION: 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? This question needs to be resolved in

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?
This question needs to be resolved in inequalities.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 = ma
:
" Four years from now she will be at most five sevenths as old as Marcia.
mi + 4 =< (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 ma
7(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 => *24
mi => 16

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