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 17 comma 800

kg of​ zucchini, 28 comma 300

kg of​ broccoli, and 38 comma 900

kg of carrots. How many packages of each style should it prepare to use up existing​ supplies?

Answer 1

Italian style = 18,000 packages

French style = 14,000 packages

Oriental style = 53,000 packages

Explanation:

See the attached figure to represent the question

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

Italian style ⇒ 0.4 kg of​ zucchini, 0.3 kg of​ broccoli, and 0.3 kg of carrots.

French style ⇒ 0.5 kg of broccoli and 0.5 kg of carrots.

Oriental style ⇒ 0.2 kg of​ zucchini, 0.3 kg of​ broccoli, and 0.5 kg of carrots.

The amount of zucchini ⇒ 17,800 = 0.4x + 0 * y + 0.2z

The amount of broccoli ⇒ 28,300 = 0.3x + 0.5y + 0.3z

The amount of carrots ⇒ 38,900 = 0.3x + 0.5y + 0.5z

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

Using the calculator:

x = 18,000 ⇒ Italian style packages

y = 14,000 ⇒ French style packages

z = 53,000 ⇒ Oriental style packages