SOLUTION: If Mary was 5 times older than Mark 10 years ago and will be twice his age in 20 years. How old are they now? I don't know how to put this into functions. Can you help me please

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Question 73899: If Mary was 5 times older than Mark 10 years ago and will be twice his age in 20 years. How old are they now?
I don't know how to put this into functions. Can you help me please
Found 2 solutions by ankor@dixie-net.com, Earlsdon:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Write an equation for each phrase; My = Mary's age now; Mk = Marks age now
:
If Mary was 5 times older than Mark 10 years ago
(My - 10) = 5(Mk-10)
:
and will be twice his age in 20 years.
(My + 20) = 2(Mk + 20)
;
How old are they now?
Using the 1st equation:
My - 10 = 5(Mk -10)
My - 10 = 5Mk - 50
My = 5Mk - 50 + 10
My = (5Mk - 40)
:
Substitute (5Mk-40) for My in the 2nd equation:
My + 20 = 2(Mk + 20)
(5Mk - 40) + 20 = 2Mk + 40
5Mk - 20 = 2Mk + 40
5Mk - 2Mk = 20 + 40
3Mk = 60
Mk = 60/3
Mk = 20 yrs is Marks present age
:
Find Mary's age using the 1st equation as rearranged to:
My = 5Mk - 40
My = 5(20) - 40
My = 100 - 40
My = 60 yrs is Mary's present age
:
Check our solution by substitution in the 2nd equation:
60 + 20 = 2(20 + 20)
80 = 80 proves our solutions
:
Did this make sense to you?

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
LET A = Mary's present age and B = Mark's present age.
10 years ago, Mary's age was A-10 and Mark's age was B-10.
From the problem description, we can write:
1) A-10 = 5(B-10) or A = 5B-40
Twenty years hence, Mary's age will be A+20 and Mark's age will be B+20.
From the problem description, we can write:
2) A+20 = 2(B+20) or A = 2B+20
Set equation 1) equal to equation 2) and solve for B (Mark's present age)
5B-40 = 2B+20 Subtract 2B from both sides.
3B-40 = 20 Add 40 to both sides.
3B = 60 Divide both sides by 3.
B = 20 This is Mark's present age.
From equation 1) we get:
A = 2B+20
A = 2(20)+20
A = 40+20
A = 60 This is Mary's present age.
Check:
A-10 = 5(B-10)
60-10 = 5(20-10)
50 = 5(10)
50 = 50
and...
A+20 = 2(B+20)
60+20 = 2(20+20)
80 = 2(40)
80 = 80