(1) The path the dog used forms two legs of a right triangle, and the hypotenuse is the straight line distance between the dog and its master=√(15²+10²) (Pythagoras). This distance is √325=5√13=18.03 ft approx.

(2) Let S, H and P be the costs of a shirt, a hat and a pin respectively.

(a) 2S+2H+4P=140,

(b) 4S+H+3P=195, so H=195-4S-3P,

(c) H+10P=70, so H=70-10P.

Therefore 195-4S-3P=70-10P, 195-70+7P=4S, S=¼(125+7P).

Substitute these values of H and S into (a):

½(125+7P)+2(70-10P)+4P=140, then double this:

125+7P+280-40P+8P=280,

125-25P=0, P=$5. So H=70-50=$20 and S=¼(125+35)=160/4=$40.

Shirt costs $40, hat costs $20 and a pin costs $5.