SOLUTION: A guy is her mom's age with digits reversed (e.g. 34 and 43). A year ago he was half her mom's age. How old are they now?
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Question 696107: A guy is her mom's age with digits reversed (e.g. 34 and 43). A year ago he was half her mom's age. How old are they now?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE ALGEBRA WAY TO SOLVE IT:
Setting up:
= first (tens) digit of that guy's age.
= second (ones) digit of that guy's age.
The guy's age is .
His mother's age is .
Last year, the guy was
and his mother was ,
which was twice the guy's age, so
Solving:
--> --> -->
At this point we could start trying values for ,
knowing that it is a small odd number.
It must be odd to make equal to the obviously odd .
It is small because it is the first digit of the son's age,
and the mother's is more than twice that, but no more than 99.
Otherwise, <-->
We see that must be a multiple of 8 plus 1.
At this point, we should see with as an obvious answer.
(Otherwise, we could try values starting with to find that only works,
because and would yield fractional values for ,
and would yield ).
Substituting into , we get
--> --> --> --> -->
The guy is and his mom is .
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