Answer:
The 3% milk quantity to be mixed is 15 liters and the the 15% cream quantity to be mixed is 5 liters
Step-by-step explanation:
The question is
Milk and cream contain different percents of butterfat. How much 3% milk needs to be mixed with how much 15% cream go give 20 L of 6% cream?
Let
x -----> the 3% milk quantity to be mixed
y -----> the 15% cream quantity to be mixed
we know that
[tex]3\%=3/100=0.03[/tex]
[tex]15\%=15/100=0.15[/tex]
[tex]6\%=6/100=0.06[/tex]
[tex]x+y=20[/tex]
[tex]x=20-y[/tex] -----> equation A
[tex]0.03x+0.15y=0.06(20)[/tex]
Multiply by 100 both sides
[tex]3x+15y=120[/tex] -----> equation B
substitute equation A in equation B and solve for y
[tex]3(20-y)+15y=120[/tex]
[tex]60-3y+15y=120[/tex]
[tex]12y=120-60[/tex]
[tex]y=60/12[/tex]
[tex]y=5\ l[/tex]
Find the value of x (equation A)
[tex]x=20-5=15\ l[/tex]
therefore
The 3% milk quantity to be mixed is 15 liters and the the 15% cream quantity to be mixed is 5 liters
