It Is Convenient To Add Salt To Butter, Produced In A Continuous Buttermaking Machine, By Adding A Slurry Of Salt With Water Containing 60% Of Salt And 40% Of Water By Weight. If The Final Composition Of The Butter Is To Be 15.8% Moisture And 1.4% Salt, E

[CUgirl]

It is convenient to add salt to butter, produced in a continuous buttermaking machine, by adding a slurry of salt with water containing 60% of salt and 40% of water by weight. If the final composition of the butter is to be 15.8% moisture and 1.4% salt, estimate the original moisture content of the butter prior to salting.

[CUgirl]

According to the solution, this is how they did it. I just don't get how they got the % moisture in the original butter at the end. PLEASE HELP AND EXPLAIN!

Textbook Solution:
Basis 100kg product
Slurry consists of 60% salt and 40% water
In the final product, there is 1.4kg salt
1.4kg is present in 2.33kg slurry
2.33kg slurry consists of 1.4kg salt and 0.93 kg water
0.93 kg water is added in the slurry to the butter

Final moisture in butter = 15.8 kg
Water added in slurry = 0.93kg
Water added in original butter = 14.87kg

Original butter in slurry/butter mix = 97.67

% moisture in original butter = 15.2%

[fiction-factory]

14.87/97.67=0.152247364
So as a % 15.2% to 3 sig figs

[fiction-factory]

I'm assuming it's that. I'm not clear about some of the terminology- e.g. what is meant by Water added in original butter

[Baldric]

Does it improve the taste of the Spam?

[Khandro]

CUgirl; Welcome to AB.

[fiction-factory]

Yes, Baldric, we noticed that two new members asked similar maths/science questions within a few minutes but unless/until someone comes along with a link to a helpful website/youtube channel then there is no harm in trying to help. I don't mind even if there is a chance it was a wasted 2 minutes

[CUgirl]

Thank you @fiction-factory! I just got stumped, as I want to understand more than just copy and paste problems I am practicing! :)