Problema Solution
A dairy farmer has two types of milk. How many gallons of a 2% milk fat solution and how many gallons of a 4.5% milk fat solution should be mixed to obtain 500 gal of a 2.9% milk solution?
Answer provided by our tutors
let
x = gallons of 2% milk fat solution
y = gallons of 4.5% milk fat solution
the fat from the first solution + the fat from the second solution = total fat
0.02*x + 0.45*y = 0.29*500
the total of milk solution is 500 thus
x + y = 500
by solving the system of equations
x + y = 500
0.02*x + 0.45*y = 0.29*500
we find
x = 186.047 gallons
y = 313.953 gallons
we need to mix 186.047 gallons of 2% milk fat solution and 313.953 gallons of 4.5% milk fat solution to obtain 500 gal of a 2.9% milk solution.