Systems with three variables

Question

Assorted nuts,bolts, and washers are packaged and sold. A package containing 1 nut, 1 bolt, and 1 washer costs 20 cents. A package containing 2 nuts, 2 bolts, and 4 washer costs 0.50. A package containing 5 nuts and 4 bolts costs 70 cents. Find the price of a nut, a bolt, and a washer.

Answer 1

N+B+W=20

2N+2B+4W =50

N+B +2W =25

subtract 1st from last equation to get

W=5 cents for a Washer

N+B=20-5 =15

multiply by5

5N+5B=75

5N+4B=70 the 3rd package

subtract to get

B=5 cents for a Bolt

N=20-5-5= 10 cents for a Nut

Nuts are 10 cents, Bolts and Washers are 5 cents each

or use matrix algebra and row operatons