SOLUTION: Please help me solve this word problem Quinn is twice as old as Karl and four years older than Parker the sum of their ages is 21. How old is Parker? Thank

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Question 822831: Please help me solve this word problem
Quinn is twice as old as Karl and four years older than Parker the sum of their ages is 21. How old is Parker? Thank you!
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
I took out the rendering braces so we can read the description and question with much less trouble.

Using p as parker
q as quinn
k as Karl

q=2k;
q=4+p;
p+q+k=21.

Substitute for q in the age sum equation; and equate the right members of the first two equations, so you'll have two equations in just p and k.
p+(2k)+k=21 and 2k=4+p;
p+3k=21 and 2k=p+4;
p+3k=21 and p-2k=-4.
Now, with these two equations, if you will subtract one of them from the other, you can quickly get a value for k. Elimination method, eliminating p.
You obtain 5k=25,
highlight%28k=5%29.

Now you can go back to the first equation for q;
q=2k
q=2*5
highlight%28q=10%29

Using second original equation,
q=4+p
10=4+p
highlight%28p=6%29

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Quinn is twice as old as Karl 
            Q = 2K

Quinn is ... four years older than Parker
            Q = P + 4

the sum of their ages is 21.
    Q + K + P = 21

So we have this system of equations:

            Q = 2K
            Q = P + 4
    Q + K + P = 21

Substitute 2K for Q in the 2nd and 3rd equations:

           2K = P + 4
   2K + K + P = 21

Simplify the second one

           2K = P + 4
       3K + P = 21

Solve the first one for P

       2K - 4 = P

Substitute in 3K + P = 21

3K + (2K - 4) = 21
  3K + 2K - 4 = 21
           5K = 25
            K = 5

Substitute 5 for K in 2K - 4 = P

     2(5) - 4 = P
       10 - 4 = P
            6 = P    <----answer!

Substitute  6 for P in Q = P + 4
 
            Q = 6 + 4
            Q = 10

Checking:

Quinn, who is 10 is twice as old as Karl, who is 5, and Quinn, who is 10,
is also four years older than Parker, who is 6. The sum of their ages is 21.
Q + P + K = 10 + 6 + 5 = 21.

So it checks.

Edwin