"Cream is approximately 22% butterfat. How many gallons of cream must be mixed w/ milk testing at 2% butterfat to get 20 gallons of milk containing 4% butterfat?"
help? thank you
c = amount of cream
m = amount of milk
20 gallons =>
c + m = 20
or m = 20 - c
20 gallons of 4% fat corresponds to 0.8 gallons of fat
=> 0.22c + 0.02m = 0.8
with m = 20 - c:
=> 0.22c + 0.02(20-c) =0.8
=> 0.22c + 0.4 - 0.02c = 0.8
=> 0.2c=0.4
=> c = 2
you need 2 gallons of cream
let x = gal of cream and y = gal of milk
then 22/100 x + 2/100 y = 4/100 (20)
or 22X + 2Y = 80 and 11 X + Y = 40 (1)
also x + y = 20 (2)
subtract (2) from (1)
10x = 20 or x = 2 therefore y = 18
we need 2 gal at 22% and 18 gal at 2% to get 20 gal at 4%
Create an equation:
x*0.22 + y*0.02 = 20*0.04
x = gallons of cream
y = gallons of milk
Now, since x + y = 20, we can replace y with 20 - x:
x*0.22 + (20 - x)*0.02 = 20*0.04
Now simplify and solve it:
11x + 20 - x = 40
10x = 20
x = 20/10
x = 2
y = 20 - x = 18
You should mix 2 gallons of cream with 18 gallons of 2% milk.
.22x+.02y=.04*20=.8
11x+y=40
x+y=20
10x=20
x=2
2 gallons cream
18 gallons milk
Comments
c = amount of cream
m = amount of milk
20 gallons =>
c + m = 20
or m = 20 - c
20 gallons of 4% fat corresponds to 0.8 gallons of fat
=> 0.22c + 0.02m = 0.8
with m = 20 - c:
=> 0.22c + 0.02(20-c) =0.8
=> 0.22c + 0.4 - 0.02c = 0.8
=> 0.2c=0.4
=> c = 2
you need 2 gallons of cream
let x = gal of cream and y = gal of milk
then 22/100 x + 2/100 y = 4/100 (20)
or 22X + 2Y = 80 and 11 X + Y = 40 (1)
also x + y = 20 (2)
subtract (2) from (1)
10x = 20 or x = 2 therefore y = 18
we need 2 gal at 22% and 18 gal at 2% to get 20 gal at 4%
Create an equation:
x*0.22 + y*0.02 = 20*0.04
x = gallons of cream
y = gallons of milk
Now, since x + y = 20, we can replace y with 20 - x:
x*0.22 + (20 - x)*0.02 = 20*0.04
Now simplify and solve it:
11x + 20 - x = 40
10x = 20
x = 20/10
x = 2
y = 20 - x = 18
You should mix 2 gallons of cream with 18 gallons of 2% milk.
.22x+.02y=.04*20=.8
11x+y=40
x+y=20
10x=20
x=2
2 gallons cream
18 gallons milk