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