Having all kinds of problems solving this one!

A group of students are asked how they travel to school.

55\% say they walk to school.

The remaining travel by car or by bus.

The ratio of students who travel by car to those who travel by bus is 2 : 3

140 more students walk than travel by bus.

How many students travel by car?

So, here is my working:

Let the total number of students in the group be n

Let the number who walk be x

Let the number who travel by car be y

Let the number who travel by bus be z

so x + y + z = n .....................(1)

11/20 n = x ............................(2) 55\%

9/20 n = y + z .........................(3) 45\%

and x - z = 140 .......................(4)

combine (2) and (3) and eliminate n

9x - 11y - 11z = 0 ......................(5)

2:3 ratio

2/5 y + 3/5 z = 0.45 n or

2/5 y + 3/5 z = 9/20 n now sub equation 1

2/5 y + 3/5 z = 9/20 (x + y + z)

8y + 12z = 9x + 9y + 9z

9x + y - 3z = 0 .....................(6)

solve (5) and (6) by subtracting

-12y - 8z = 0 so y = -2/3 z ......(7)

sub (4) and (7) into (6)

9(140 + z) -2/3 z - 3z = 0

1260 + 27/3 z - 11/3 z = 0

1260 + 16/3 z = 0 so z = -236.25

and already I feel like I am wrong. I am expecting positive integer results. Is the method wrong or have I made an arithmetic error?

Thanks