1. Trouble Understanding Word Problems

Hi everyone, I am having trouble wrapping my head around a few word problem examples and I have been reading my book over and over and cannot even begin to get anywhere with them.

Example 1:
20 peperoni pizzas were delivered at a total cost of $181. A sm. pizza costs$5 (contains 3oz. of pepperoni)
A med. pizza costs $9 (contains 4oz. of pepperoni) A lrg pizza costs$12 (contains 5oz. of pepperoni)
5lbs 2 ounces of pepperoni were used in making these 20 pizzas.
How many pizzas of each size were delivered?

Example 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?

Example 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?

2. Originally Posted by lanipr
Example 1:
20 peperoni pizzas were delivered at a total cost of $181. A sm. pizza costs$5 (contains 3oz. of pepperoni)
A med. pizza costs $9 (contains 4oz. of pepperoni) A lrg pizza costs$12 (contains 5oz. of pepperoni)
5lbs 2 ounces of pepperoni were used in making these 20 pizzas.
How many pizzas of each size were delivered?
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

Example 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?
let A = number of packets of mixture 1
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

Example 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?
let v = no wind speed of airplane
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

3. Thank you!