John is 6 years older than keisha. together, their ages equal four times keisha's age. how old is each? (note: there must be an equation written using the variable x, and x must be solved.)

k= Keisha  
k + 6= John          
k + k + 6 =  4k   
2k + 6 ( - 2k) =  4k ( - 2k)               
6 = 2k            
3 = k    
(Keisha= 3 years old)          
k + 6 = 9    
(John = 9 years old)

3 + 3 + 6 = 4 (3)          
12 = 12

So we made the pawn represent Keisha’s age.  Then we knew that John is 6 years older than Keisha so we represented his age with a pawn plus 6. This went on 1 side of the equation because it said that together they equal 4 times Keisha’s age. So on the other side of the equation we put 4 pawns because we are using each pawn as Keisha’s age.  Then we subtracted the pawns from each side to keep the equation balanced.  So we had that 2 pawns equal 6, which means that each pawn equals 3 so Keisha is 3 years old.  Since John is 6 years older than Keisha, he must be 9 years old.  We checked our work and substituted 6 in for each pawn and found that 12 equals 12, so our equation is balanced.

Hope this helps :)

Let x= Keisha
x+6= John
together means to add
x+x+6= 4x combine like terms
2x+6=4x
subtract 2x from both sides
6= 2x
divide both sides by 2
 3=x  Keisha's age
3+6= 9 John"s age

Proof  3+9= 4x3

hope this helps