mixture problem

a chef mixes three types of salt and vinigar solutions to make 100 pounds of solution that is 30% salt and 30% vinigar. type a is 20$ salt and 30%vingar, type b is 20% salt and 10% vingar, type c is 60% sail and 20% vinigar. how many pounds of each should be mixed?

let x = pounds of type a,
 
y = pounds of type b, and
 
z = pounds of type c.
 
 
from the description of the problem, write down what is given:
 
 
    x  +     y +      z = 100
 
0.2x + 0.2y + 0.6z =   30
 
0.3x + 0.1y + 0.2z =   30
 
 
 
using the equation solver on a calculator,
 
x = 87.5 pounds
 
y = -12.5 pounds
 
z = 25 pounds
 
note that we can't have a negative mass for the answer (type b), so it's not possible to make the mixture with the given solutions.