This stuff kills me

Question

1.) A math teacher tried to teach his dog to play fetch. The dog started next to his master, then ran fifteen feet south, picked up the squeaky tennis ball, walked ten feet east, and sat down to chew on the ball. At that point, how far apart were the dog and his master?

2.) In a happier time, when families could safely go to amusement parks, one particular world-famous park sold t-shirts, hats, and commemorative pins. One family bought two shirts, two hats, and four pins. They paid $140. Another family bought four shirts, one hat, and three pins. They paid $195. One collector didn’t buy a shirt, but they bought one hat and ten pins to put on it. They paid $70. How much did a shirt cost? A hat? A pin?

Answer 1

(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.