MHB Solve Milk & Cream Mixture Word Problem: Help Needed

[paulmdrdo1]

can you explain what the problem is asking for?
please use single variable only.

One thousand quarts of milk testing 4% butterfat are to be reduced to 3%. How many quarts of cream testing 23% butterfat must be separated from the milk to produce the required result? All percentages are by volume.

please help. I'm confused.

 

[MarkFL]

First determine the amount in quarts of pure fat with which we have to work. Let $x$ be the amount of cream in quarts to be removed. Then set the amount of fat in the resulting 3% mix of milk plus the amount of fat in the result 23% mix of cream equal to the total amount of fat and solve for $x$. What equation do you get?

 

[paulmdrdo1]

the amount of butterfat is 1000(0.04) = 40 quarts

but I don't know what's the component here. the problem says that the percentage of butterfat in the 1000 quarts of milk is 4%, but if we remove some cream it is 23% butterfat? why is that?

 

[MarkFL]

Apparently when the cream rises, it consists of 23% fat. So when we remove $x$ quarts of cream, how many quarts of milk is left?

 

[paulmdrdo1]

Hmmm...

I'm confused about that cream. Is there an amount of cream in the 1000 quarts of milk with which 4% is butterfat? please bear with me. English is not my primary language.

can you tell what's happening in the problem? although I understand what we are asked to find here. What's with "milk testing" and "cream testing"? there are terms that I don't understand.

because If there's an amount of cream to begin with, the percentage of the butterfat in the amount of cream to be removed should also contain 4%. that's how I view the problem. how come that it has 23% butterfat?

 

[MarkFL]

I would focus on the algebra rather than the chemistry here. :D Whether this is a realistic problem involving milk fat or not, I really couldn't tell you. Just imagine that somehow through some process cream can be extracted from the milk that contains 23% milk fat. :D

 

[paulmdrdo1]

yeah you're right! I think I'm over-thinking it.

anyways if I just focus on the algebra this is how I would solve it

$0.04(1000) = 40$ quarts - amount BF in 1000 quarts of milk.

$0.23x =$ amount of BF in the cream to be removed from the 1000 quarts milk.

$1000-x = $new volume of milk

we wish to have a post-removal volume percentage of 3%.

then,

$0.04(1000)-0.23x=(1000-x)0.03$

$x=50$ quarts of cream should be removed. is this correct? thanks!

 

[MarkFL]

Yep, you got it! (Cool)