Next year C will be half the age of G. G will be 6 years older than C next year. How old is G this year?

Question

Next year Charlie will be half the age of Gwen. Gwen will be 6 years older than Charlie next year. How old is Gwen this year?

Answer 1

C = Charlie's age; G = Gwen's age.

 

Next year, C = (1/2)(G)  ("of" means "multiply" in a word problem, so "half of Gwen's age" means multiply Gwen's age by 1/2).

 

Also next year, G = C+6.

 

Multiply both sides of the first equation by 2, to get rid of the 1/2.  Then instead of C = (1/2)(G), we have 2C = G.

 

Now we have two equations in terms of G:  G = C+6 and G =2C.   Since both C+6 and 2C are equal to G, they must be equal to each other.  C+6 = 2C.  Subtract C from both sides:  6 = C.

 

So next year, Charlie will be 6 and Gwen will be 12 (6 years older than Charlie).  This year, Gwen is 11.