SOLUTION: Clark is twice as old as Matt. In two years the sum of their ages will be five times as much as what Matt's age was four years ago. How old is each now?

Algebra ->  Test -> SOLUTION: Clark is twice as old as Matt. In two years the sum of their ages will be five times as much as what Matt's age was four years ago. How old is each now?      Log On


   

Question 987959: Clark is twice as old as Matt. In two years the sum of their ages
will be five times as much as what Matt's age was four years ago.
How old is each now?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Since Mark and Matt have names that start with the same first 
letter I have changed Mark's name to Clark.

Clark is twice as old as Matt. In two years the sum of their
ages will be five times as much as what Matt's age was four
years ago. How old is each now?

Clark is twice as old as Matt. 
C = 2M

In two years the sum of their ages... 
In two years Clark will be C+2 and Matt will be M+2 and 
the sum of their ages will (C+2)+(M+2) which equals 

C+M+4     <-- sum of their ages in two years.

...will be five times as much as what Matt's age was four
years ago. 
M-4       <-- what Matt's age was four years ago.

So we are told that C+M+4 is 5 times as much as M-4.  So

C+M+4 = 5(M-4)

Now we have this system of equations to solve:

system%28C=2M%2CC%2BM%2B4=5%28M-4%29%29

Simplify and solve this system by substitution.

Edwin