Question

A company produces three combinations of mixed vegetables that sell in​ 1-kg packages. Italian style combines 0.4 kg of​ zucchini, 0.3 kg of​ broccoli, and 0.3 kg of carrots. French style combines 0.5 kg of broccoli and 0.5 kg of carrots. Oriental style combines 0.2 kg of​ zucchini, 0.3 kg of​ broccoli, and 0.5 kg of carrots. The company has a stock of 18 comma 200 kg of​ zucchini, 28 comma 100 kg of​ broccoli, and 38 comma 700 kg of carrots. How many packages of each style should it prepare to use up existing​ supplies?

Answer 1

Italian style = 19,000 packages

French style = 13,000 packages

Oriental style = 53,000 packages

Explanation:

let the number of packages of Italian style = x

let the number of packages of French style = y

let the number of packages of Oriental style = z

See the attached table which summarize the problem

Using the table we can get the following system of equations:

0.4x + 0 * y + 0.2z = 18,200

0.3x + 0.5y + 0.3z = 28,100

0.3x + 0.5y + 0.5z = 38,700

Solving the 3 equations together to find x , y and z

Using the calculator

x = 19,000

y = 13,000

z = 53,000