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
B-4 = (1/2) (C-4) = (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
B-4 = (1/2) (C-4) = (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 *(c-4) which is 1/2C-4/2 or simply 1/2c-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 *(c-4) which is 1/2C-4/2 or simply 1/2c-2
these questions become easy if you organize your data in a chart form
------------Byte-----Cathy
Age now ---- b ------ c
in 4 yrs -- b+4 ---- c+4
4 yrs ago-- b-4 ---- c-4
so from second line: b+4 = 3/4(c+4)
from third line: b-4 = 1/2(c-4)
These two equations are now easy to simplify and solve giving you the answer provided by drwls above
To solve this two-variable word problem, let's first assign variables to the ages of Cathy and her cat. Let's say Cathy's age is represented by 'C' and Byte's age is represented by 'B'.
According to the problem, "In four years, Cathy's cat Byte will be three-fourths as old as Cathy will be." This can be written as an equation:
(B + 4) = (3/4)(C + 4)
The second piece of information given is, "Four years ago, Byte was only half as old as Cathy was." This can be expressed as the equation:
(B - 4) = (1/2)(C - 4)
Now, we have a system of two equations with two variables, and we can solve it.
1. Expand the first equation:
B + 4 = (3/4)C + 3
2. Expand the second equation:
B - 4 = (1/2)C - 2
3. Rearrange both equations to isolate 'B':
B = (3/4)C - 1
B = (1/2)C + 2
Notice that both equations are already isolated for 'B' on one side.
Now, we can set these two equations equal to each other since they both represent 'B':
(3/4)C - 1 = (1/2)C + 2
Let's solve this equation algebraically:
4(3/4)C - 4(1) = 4(1/2)C + 4(2)
3C - 4 = 2C + 8
Simplifying further:
3C - 2C = 8 + 4
C = 12
So, Cathy's current age is 12.
To find Byte's age, we substitute the value of C into either of the original equations. Let's use the first equation:
B = (3/4)(C) - 1
B = (3/4)(12) - 1
B = 9 - 1
B = 8
Therefore, Cathy is currently 12 years old, and her cat Byte is 8 years old.