SOLUTION: Tim is 6 years older than Scott. Mike's age is 3 times Tim's age. The sum of Tim and Scott's age is 17 years less than Mike's, how old is Scott?

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Question 1167835: Tim is 6 years older than Scott. Mike's age is 3 times Tim's age. The sum of Tim and Scott's age is 17 years less than Mike's, how old is Scott?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
TIM t
SCOTT s
MIKE m

system%28t=s%2B6%2Cm=3t%2Ct%2Bs=m-17%29


notice that s=t-6.



t%2Bs=m-17
t%2Bt-6=3t-17----------one equation, one variable; question asked for s, but this equation was easy enough to form.
.
.
.
s=5
Scott is 5.

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
Tim is 6 years older than Scott. Mike's age is 3 times Tim's age.
The sum of Tim and Scott's age is 17 years less than Mike's, how old is Scott?
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Let Scott's age be x years.


Then Tim's age is (x+6) years;  Mike's age is 3*(x+6).


According to the condition,


    x + (x+6) = 3*(x+6) - 17.


Simplify and find x


    2x + 6 = 3x + 18 - 17

    2x + 6 = 3x + 1

    6 - 1 = 3x - 2x

    x = 5  years is the Scott's age.    ANSWER

Solved.

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It is a typical problem to be solved using only one unknown.