math
posted by jason .
In four years Cathy¡¯s cat Byte will be three fourths as old as Cathy will be. Four years ago, Byte was only half as old as Cathy was. How old are Cathy and her cat?
I am struggling to solve this two variable word problem.
please help.

C be Cathy's age now and B be Byte's age now.
B+4 = (3/4) (C+4) = (3/4) C + 3
B4 = (1/2) (C4) = (1/2) C  2
Subtract the two equations (left and right sides separately)
8 = (1/4) C + 5
C/4 = 3
C = 12
Use either of the first equations to get B. 
in B+4 = (3/4) (C+4) = (3/4) C + 3
B4 = (1/2) (C4) = (1/2) C  2
may I ask where you got the +3 and 2? 
the +3 comes from...
(3/4)*(c+4)
which is another way of saying
((3/4)*c)+(3/4*4)
or
3/4C+(12/4)
3/4C+3
The 2 comes from multiplying 1/2 *(c4) which is 1/2C4/2 or simply 1/2c2 
the +3 comes from...
(3/4)*(c+4)
which is another way of saying
((3/4)*c)+(3/4*4)
or
3/4C+(12/4)
3/4C+3
The 2 comes from multiplying 1/2 *(c4) which is 1/2C4/2 or simply 1/2c2 
these questions become easy if you organize your data in a chart form
ByteCathy
Age now  b  c
in 4 yrs  b+4  c+4
4 yrs ago b4  c4
so from second line: b+4 = 3/4(c+4)
from third line: b4 = 1/2(c4)
These two equations are now easy to simplify and solve giving you the answer provided by drwls above 
BUTTCHEEKS!!!!!!!