SOLUTION: Reversing the digits of Gyver's age gives Ed's age with a difference of 18 years. If the sum of the digits of each age is 6, how old is Gyver? Thanks a bunch for answering this

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Reversing the digits of Gyver's age gives Ed's age with a difference of 18 years. If the sum of the digits of each age is 6, how old is Gyver? Thanks a bunch for answering this       Log On


   

Question 752451: Reversing the digits of Gyver's age gives Ed's age with a difference of 18 years. If the sum of the digits of each age is 6, how old is Gyver?
Thanks a bunch for answering this :)
Answer by MathTherapy(10858) About Me  (Show Source):
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Reversing the digits of Gyver's age gives Ed's age with a difference of 18 years. If the sum of the digits of each age is 6, how old is Gyver?
Thanks a bunch for answering this :

Based on info, Gyver is YOUNGER than Ed

Let the tens and units digits of Gyver’s age be T and U, respectively
Then: 10T + U = 10U + T – 18 ------ 10T – T + U – 10U = - 18 ----- 9T – 9U = - 18 ---- 9(T – U) = 9(- 2)
T – U = - 2 ------ eq (i)
Also, T + U = 6 ----- eq (ii)
2T = 4 ------ Adding eqs (i) & (ii)
T, or tens digit of Gyver’s age = 4%2F2, or 2

2 – U = - 2 ------ Substituting 2 for T in eq (i)
- U = - 2 – 2
- U = - 4
U, or units digit of Gyver’s age = %28-+4%29%2F-+1, or 4

Therefore, Gyver is highlight_green%2824%29 years-old

You can do the check!!

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