SOLUTION: A father's age is formed by reversing the two digits of son's age. If the father is 27 years older than his son and sum of the digits used is 7, Find their age.

Algebra ->  Equations -> SOLUTION: A father's age is formed by reversing the two digits of son's age. If the father is 27 years older than his son and sum of the digits used is 7, Find their age.       Log On


   

Question 1134290: A father's age is formed by reversing the two digits of son's age.
If the father is 27 years older than his son and sum of the digits used is 7,
Find their age.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Father, 10t%2Bu
Son, t%2B10u

system%2810t%2Bu=t%2B10u%2B27%2Ct%2Bu=7%29

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9t-9u=27
t-u=3

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system%28t%2Bu=7%2Ct-u=3%29
.
.
system%28t=5%2Cu=2%29
Father is 52 and son is 25.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A father's age is formed by reversing the two digits of son's age.
t = tens digit of Son's age
u = ones digit of Son's age
Son's age = 10t+u
Father's age = 10u+t
If the father is 27 years older than his son
(Father's age) = (Son's age) + 27
    10u+t      =   10t+u     + 27
         10u+t = 10t+u + 27
         9u-9t = 27
           u-t = 3
and sum of the digits used is 7
u+t = 7

Add the two equations:

 u-t = 3
 u+t = 7 
---------
2u   = 10
   u = 5

u+t = 7
5+t = 7
  t = 2

Son's age = 10t+u = 10(2)+5 = 20+5 = 25
Father's age = 10u+t = 10(5)+2 = 50+2 = 52.

Or you could just write down the digits t and u:

Son's age = "t and then u" = 25
Father's age "u and then t" = 52

Edwin