Question

A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 5% real fruit juice. The company used 56.5 liters of real fruit juice to make 80 more liters of Drink B than liters of Drink A. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.

Answer 1

Answer:

Therefore the company made 510 liters of Drink A and (510+80)=590 liters of Drink B.

Step-by-step explanation:

Let, the company make x liters of drink A

The company makes drink B of (80+x) liter. Since the company make 80 more liters of Drink B than liters Drink A .

Given drink A contains 20% real fruit.

Therefore x liters of drink A contains $=\frac{20}{100}\times x$ liters$=\frac{x}{5}$ liters real fruit.

Drink B contains 5% real fruit juice.

(80+x) liters of drink B contains $=\frac{5}{100}\times (80+x)$ liters $=\frac{80+x}{20}$ liter real fruit.

The company used 56.5 liters of real fruit juice to make Drink A and Drink B.

According to the problem,

$\frac{80+x}{20}+\frac{x}{5}= 56.5$

$\Rightarrow \frac{80+x+4x}{20}=56.5$

⇒80+5x = 56.5×20

⇒80+5x=1130

⇒5x=1130-80

⇒5x=1050

$\Rightarrow x=\frac{1050}{5}$

⇒x=510

Therefore the company made 510 liters of Drink A and (510+80)=590 liters of Drink B.