SOLUTION: Three years ago, Mark was twice as old as Diane. Four years from now, twice Mark's age will be three less than three times Diane's age. How old are they now?

Question 1046202: Three years ago, Mark was twice as old as Diane. Four years from now, twice Mark's age will be three less than three times Diane's age. How old are they now?
Please help me solve this problem.
Thank you very much for your cooperation.
Email: kwame730@gmail.com
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let m = Marks present age
let d = diane's
:
Write an equation for each statement, simplify as much as possible
:
Three years ago, Mark was twice as old as Diane.
m - 3 = 2(d - 3)
m - 3 = 2d - 6
m = 2d - 6 + 3
m = 2d - 3
:
Four years from now, twice Mark's age will be three less than three times Diane's age.
2(m+4) = 3(d+ 4) - 3
2m + 8 = 3d + 12 - 3
2m = 3d + 9 - 8
2m = 3d + 1
replace m with (2d - 3) from the first statement
2(2d-3) = 3d + 1
4d - 6 = 3d + 1
4d - 3d = 6 + 1
d = 7 yrs is Diane's present age
then
m = 2(7) - 3
m = 11 yrs is Marks age
:
;
You can check this for yourself in both statements

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