Math word problem please help

Question

Grace had 16 more comic books then Mark. After Mark gave Grace 12 of his comic books he realized he then had half as many as Grace. How many comic books did grace end up with ?

Answer 1

Gracie has 16 more than Mark, written thusly:  Gracie = Mark + 16

 

Mark gives Gracie 12 comic books, so add 12 to Gracie and subtract 12 from Mark

Gracie + 12  ?  Mark - 12

 

For the ?, the question is, what happened after we did this?  Mark has half as many as Gracie.  This means if I were to double Mark's comics, they'd be equal again

 

Gracie + 12 = 2 * (Mark - 12)

G + 12 = 2*(M - 12)

G + 12 = 2M - 24

G + 36 = 2M

G = 2M - 36

 

Going back to our first equation now:

G = M + 16

 

  G = 2M - 36

-(G = M + 16)

 0 = M - 52

M = 52

 

G = 52 + 16

G = 68.

 

Recapping by going over the initial word problem, but filling in the numbers:

 

Gracie has 68 comic books (16 more than Mark, because Mark has 52).  After Mark gave Gracie 12 (leaving him 40 and her 80) he realized he had half as many as grace.