A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 15% real fruit juice. The company used 100.5 liters of real fruit juice to make 30 more liters of Drink A than liters of Drink B. 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.

A linear equation system is a set of linear equations that have more than one unknown. The unknowns appear in several of the equations, which relate the unknowns or variables to each other.

In this case the equation system contains 2 equations with two variables. To determine what the system is, determine what the variables will be:

x = amount of real fruit juice used to make Drink A
y = amount of real fruit juice used to make Drink B

You know that the company used 100.5 liters of real fruit juice (to make Drink A and Drink B), so:

x+y=100.5

On the other side, you know that Drink A contains 20% real fruit juice. 20 % is the same that [tex]\frac{20}{100} =\frac{1}{5}[/tex]

Then

x=[tex]\frac{1}{5}[/tex]*amount of drink A produced → 5*x = amount of drink A produced

And you know that Drink B contains 15% real fruit juice. 15 % is the same that [tex]\frac{15}{100} =\frac{3}{20}[/tex]

Then

y=[tex]\frac{3}{20}[/tex]*amount of drink B produced → [tex]\frac{20}{3}[/tex]*y=amount of drink B produced

Finally, you know that the company makes 30 more liters of Drink A than liters of Drink B. This is:

[tex]5*x=30+\frac{20}{3} *y[/tex]

It is the same as saying that the difference between the production of Drink A and Drink B must be 30:

[tex]5*x-\frac{20}{3} *y=30[/tex]

So,by combining both equations, the system of two equations is:

[tex]\left \{ {{x+y=100.5} \atop {5*x-\frac{20}{3}*y =30}} \right.[/tex]