Question 778755: The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages
Found 2 solutions by DrBeeee, ankor@dixie-net.com:
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let Jack's age = ab,
Then Bill's age = ba
In five years we have
(1) ab + 5 = 2*(ba +5) or
(2) ab = 2*ba + 5
Jack's age of ab can be written as
(3) ab = 10*a + b and Bill's age is
(4) ba = 10*b + a
Put (3) and (4) into (2) and get
(5) 10*a + b = 2*(10*b + a) + 5 or
(6) 10*a - 2*a = 20*b - b + 5 or
(7) 8*a = 19*b + 5
Now we must find integers use (7) a and b that satisfy (7). If we let
(8) b = {0,1, 2,...,9} and use (7) to find a, we only get the integer pair
(9) (a,b) = (3,1)
Let's check this answer with (1).
Is (31 + 5 = 2*(13 + 5))?
Is (36 = 2*18))?
Is (36 = 36)? Yes
Answwer: The difference between Jack's age and Bill's age is 18.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order.
In five years Jack will be twice as old as Bill will be then.
What is the difference in their current age?
:
Let a = 10's digit in Jack's age
Let b = units digit " " "
then
10a+b = Jack's current age
and
10b + a = Bill's
:
"In five years Jack will be twice as old as Bill will be then. "
10a + b + 5 = 2(10b + a + 5)
10a + b + 5 = 20b + 2a + 10
10a - 2a = 20b - b + 10 - 5
8a = 19b + 5
Now we have two unknowns with a single equation, however we know:
Jack is older than Bill, therefore a > b
a and b have to be single digits. (1 thru 9)
Assume b = 1
8a = 19(1) + 5
8a = 24
a = 24/8
a = 3
Then Jack is 31, Bill is 13
"What is the difference in their current age?"
31 - 13 = 18 (the difference between reversed numbers is always a multiple of 9)
:
:
Check this in the statement:
""In five years Jack will be twice as old as Bill will be then. "
31 + 5 = 2(13+5)
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