9 gal=amount of water to be added with 0% concentration of sugar

x=gal of 40% sugar solution

23%=final solution

(9gal)(0)+(x)(40%)=23%(x+9gal)

0+(x)(40%)=23%(x+9gal)

0+(x)(40%)=23%(x) (23%)(+9gal)

(x)(40%)=23%(x) + (207%gal)

(x)(40%)-23%x=23%(x)-23%x + (207%gal)

17%x=207%gal

17%x/17%=207%gal/17%

x=12.18gal