linear system help?

[Kai]

I wasn't quite sure where to post this, but here I go.
I need to prepare a 5L of a liquid with 33% alcohol, I have liquids with 30 and 35% alcohol respectively, so obviously I need 3L of 35% and 2L of 30%.
But how do I solve this problem using a linear system?

 

[Mrspi]

I wasn't quite sure where to post this, but here I go.
I need to prepare a 5L of a liquid with 33% alcohol, I have liquids with 30 and 35% alcohol respectively, so obviously I need 3L of 35% and 2L of 30%.
But how do I solve this problem using a linear system?

Start by defining the variables you are going to use:

let x = number of liters of 30% solution
let y = number of liters of 35% solution

We want to end up with a total of 5 L of the new solution, so

x + y = 5

The amount of alcohol in x liters of 30% solution is 0.30x.
The amount of alcohol in y liters of 35% solution is 0.35y
The amount of alcohol at the end is 33% of the 5 L, or 0.35(5)

.30x + .35y = 0.33(5)<-------edited to fix a typo here

Those equations constitute your system....solve it by your favorite method.

If you are still having trouble, please respond, showing us your work.

 

[Kai]

Thank you, with this I managed to figure it out. I had everything the same as you except at the end I had
0.33 instead of .33(5) which is what I'm sure you meant.
Thank you very much!