SOLUTION: Dan is 5 times as old as mike. in 7 years dan will be 2 more than 3 times as old as mike. find their present ages.

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Question 118288: Dan is 5 times as old as mike. in 7 years dan will be 2 more than 3 times as old as mike. find their present ages.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = Dan's; present age
Let m = Mike's present age
:
Just write an equation for what it says:
"Dan is 5 times as old as mike. "
d = 5m
:
In 7 years we have:
(d+7)
and
(m+7)
:
"in 7 years dan will be 2 more than 3 times as old as mike."
d + 7 = 3(m+7) + 2
d + 7 = 3m + 21 + 2
d + 7 = 3m + 23
d = 3m + 23 - 7
d = 3m + 16
:
We know that d = 5m; substitute 5m for d and solve for m
5m = 3M + 16
5m - 3m = 16
2m = 16
m = 16/2
m = 8
therefore
d = 5(8) = 40
:
:
Check solution in the statement:
"in 7 years dan will be 2 more than 3 times as old as mike."
40 + 7 = 3(8+7) + 2
47 = 3(15) +2; confirms out solution