SOLUTION: pat is 22 years older than his son Patrick . in 9 years pat will be twice as old as patrick. how old are they now ?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: pat is 22 years older than his son Patrick . in 9 years pat will be twice as old as patrick. how old are they now ?      Log On


   

Question 1165675: pat is 22 years older than his son Patrick . in 9 years pat will be twice as old as patrick. how old are they now ?
Found 3 solutions by josgarithmetic, Edwin McCravy, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
x, Patrick
y, Pat
system%28y=x%2B22%2Cy%2B9=2%28x%2B9%29%29

%28x%2B22%29%2B9=2x%2B18
.
.
.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Pat is 22 years older than his son Patrick. In 9 years Pat will be twice as
old as Patrick. how old are they now ?
"Pat" ends with the letter "t",
so let t = Pat's age.
"Patrick" ends with "k", 
so let k = Patrick's age.
Pat is 22 years older than his son Patrick.
Therefore 

         t = k + 22
In 9 years Pat will be twice as old as Patrick [WILL BE].

     t + 9 = 2(k + 9)

Since t = k + 22, we can substitute "k + 22" for t in this:

     t + 9 = 2(k + 9)

k + 22 + 9 = 2(k + 9)

    k + 31 = 2k + 18
              
        13 = k 

So Patrick is 13

Now you can substitute 13 for k in this:

         t = k + 22
         t = 13 + 22
         t = 35

Edwin

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Without algebra (if an algebraic solution is not required)....

The difference in their ages is 22.

So when Pat is twice as old as Patrick, their ages will be 22 and 44.

Since that will be 9 years from now, their current ages are 13 and 35.