SOLUTION: Five years ago, John was three times older than Jack. Today, John is just twice as old as Jack. How old is John today? How old was Jack 5 years ago?

Question 334997: Five years ago, John was three times older than Jack. Today, John is just twice as old as Jack. How old is John today? How old was Jack 5 years ago?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let n = John's present age
Let k = Jack's present age
:
Write an equation for each statement and simplify:
:
Five years ago, John was three times older than Jack."
n - 5 = 3(k-5)
n - 5 = 3k - 15
n = 3k - 15 + 5
n = 3k - 10
:
Today, John is just twice as old as Jack.
n = 2k
:
How old is John today?
Replace n with 2k in the 1st simplified equation
2k = 3k - 10
2k - 3k = -10
-k = -10
k = 10 yrs is Jack's age today
then
2(10) = 20 yrs is John's present age
;
How old was Jack 5 years ago
10 - 5 = 5 yrs is Jack's age 5 yrs ago
:
:
Check solution in the statement:
"Five years ago, John was three times older than Jack. "
20 - 5 = 3(10 - 5); confirms our solutions
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