ABC is a triangle. |BC|=a units,|CA|=b units, |AC|=c units.

2a+b+c=24

2a+2c=29

How many integer values a can assume ?

My work:

a+c=14.5

c-b=5

a>c-b=5

b+c>a

b+c=24-2a

24>3a

8>a>5 is my answer and there are 2 values. But according to the book there are 3 values.