SOLUTION: Please help with this problem it doesn't make sence. Peggy is 6 years younger than Rosa. Two years from now, Peggy will be twice as old as Rosa. Find their present ages.

Question 55412: Please help with this problem it doesn't make sence.
Peggy is 6 years younger than Rosa. Two years from now, Peggy will be twice as old as Rosa. Find their present ages.
Found 2 solutions by stanbon, foleysdad:
Answer by stanbon(48546) (Show Source):
You can put this solution on YOUR website!
Peggy is 6 years younger than Rosa. Two years from now, Peggy will be twice as old as Rosa. Find their present ages.
-----------
Ages NOW DATA:
Let Rosa's age be "x" yrs.
Then Peggy' age is "x-6" yrs.
Comment: Peggy is younger than Rosa.
---------
2 years from now DATA:
Rosa will be x+2 yrs old
Peggy will be x-4 yrs old
Comment: Peggy is still younger than Rosa
---------------
EQUATION:
Peggy will be twice as old as Rosa.
CAN'T BE
You're right; makes no sense.
cheers,
Stan H.

Answer by foleysdad(7) (Show Source):
You can put this solution on YOUR website!
I am guessing that the question is wrong and it should read:
Peggy is 6 years younger than Rosa. Two years from now Rosa will be twice as old as Peggy. Let's face it Peggy can never be older than Rosa unless Rosa dies and then it would be a stupid question.
To solve the question as I have restated it.
You have two variables the current ages of Peggy and Rosa. For my solution P will be Peggy's current age and R will be Rosa's current age.
Since I have 2 variables, I need 2 equations.
R = P + 6 From statement one
R + 2 = 2(P+2) From statement two
Now substitute from equation one into equation two.
(P+6) + 2 = 2(P+2)
P + 8 = 2P + 4 Now subtract P from both sides
8 = P + 4 Now subtract 4 from both sides
4 = P
Since P=4 then R = 10, let's check the other equation.
P+2 = 6 and R+2 = 12 and you can see that R in two years is double P in two years.