Question 73899
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?