SOLUTION: Michelle is eight years older than Adam. Three years ago Michelle was twice as old as Adam was then. How old is Michelle?

Question 106045: Michelle is eight years older than Adam. Three years ago Michelle was twice as old as Adam was then. How old is Michelle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement:
:
"Michelle is eight years older than Adam."
M = A + 8
:
"Three years ago"
They would be:
(M-3)
and
(A-3)
:
Three years ago Michelle was twice as old as Adam was then.
M - 3 = 2(A-3)
M - 3 = 2A - 6
M = 2A - 6 + 3
M = 2A - 3
:
How old is Michelle?
Substitute (A+8) for M (from the 1st statement
A + 8 = 2A - 3
8 + 3 = 2A - A
11 = A
A is 11 yrs old now
then
M =11 + 8 = 19 yrs old now
:
:
Check our solution using the statement:
"Three years ago Michelle was twice as old as Adam was then."
(19 - 3) = 2(11 - 3)
16 = 2(8); confirms our solution
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