let S = number of small pizzas

M = number of medium pizzas

L = number of large pizzas

S + M + L = 20

S($5) + M($9) + L($12) = $181

S(3 oz) + M(4 oz) + L(5 oz) = 82 oz

solve the system of equations for S, M, and L

let A = number of packets of mixture 1Example 2:

A dietician has two prepackaged mixtures of vitamin additives available for patients. Mixture 1 contains 5 grams of vitamin C and 3 grams of niacin; mixture 2 contains 6 grams of vitamin C and 5 grams of niacin. On an average day she needs 87 grams of niacin and 117 grams of vitamin C. How many packets of each mixture will she need?

B = number of packets of mixture 2

A(5 g) + B(6 g) = 117g of vitamin C

A(3 g) + B(5 g) = 87g of niacin

solve the system for A and B

let v = no wind speed of airplaneExample 3:

A twin-engined aircraft can fly 1500 miles from city A to city B in 5 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind and the speed of the plane without any wind?

w = wind speed

rate x time = distance

with the wind ...

(v + w)5 = 1500

v + w = 300

against the wind ...

(v - w)6 = 1500

v - w = 250

solve the system for v and w