A baker uses dried skim milk that contains 3.0% moisture and costs $1.16 per lb, which on a moisture free basis would be $1.20 per lb. If liquid skim milk containing 90.5% water costs $1.60 per gallon (8.64 lbs), what would be the comparative cost of 1lb. dry solids from the liquid milk?
Here is how the 3% stuff is calculated.
3% moisture = 97% milk; therefore,
1.16 x (100%/97%) = 1.20
So wouldn't we do the liquid milk the same way?
1.60 x (100/9.5) = ??/8.64 lbs.
So the cost per 1 lb is xx.
so you have to find the percentage moisture loss
To find the comparative cost of 1lb. dry solids from the liquid skim milk, we need to consider the moisture content in both types of skim milk.
Let's assume that 1lb of dried skim milk contains X lb of dry solids and Y lb of moisture. We can calculate the values of X and Y using the given information.
The dried skim milk contains 3.0% moisture, which means it contains 97.0% dry solids. So, for every 1lb of dried skim milk, we have:
Dry solids = 97/100 * 1lb = 0.97 lb
Moisture content = 3/100 * 1lb = 0.03 lb
Now, let's compare this with the liquid skim milk:
Liquid skim milk contains 90.5% water, which means it contains 9.5% dry solids. So, for every 8.64 lbs of liquid skim milk (which is equivalent to 1 gallon), we have:
Dry solids = 9.5/100 * 8.64 lbs = 0.8208 lb
Water content = 90.5/100 * 8.64 lbs = 7.8192 lb
Now, we can calculate the comparative cost of 1lb of dry solids from the liquid skim milk.
The cost of 1lb of dried skim milk on a moisture-free basis is $1.20.
Since 1lb of dried skim milk contains 0.97 lb of dry solids, the cost per lb of dry solids from the dried skim milk is:
Cost per lb of dry solids from dried skim milk = $1.20 / 0.97 lb = $1.2371 per lb of dry solids
Now, we need to find the comparative cost of 1lb of dry solids from the liquid skim milk.
Since 8.64 lbs of liquid skim milk contains 0.8208 lb of dry solids, the cost per lb of dry solids from the liquid skim milk is:
Cost per lb of dry solids from liquid skim milk = $1.60 / 0.8208 lb = $1.9497 per lb of dry solids
Therefore, the comparative cost of 1lb of dry solids from the liquid skim milk is $1.9497.
To find the comparative cost of 1lb. dry solids from the liquid milk, we need to compare the costs of the two types of skim milk on a dry solids basis.
Let's start by calculating the cost of the dried skim milk per pound of dry solids. We know that the dried skim milk contains 3.0% moisture, meaning it consists of 97.0% dry solids. Since the cost of the dried skim milk on a moisture-free basis is $1.20 per pound, the cost per pound of dry solids would be:
Cost per pound of dry solids = Cost per pound on a moisture-free basis / Percentage of dry solids
Cost per pound of dry solids = $1.20 / 97.0% = $1.24
Next, let's calculate the cost of the liquid skim milk (containing 90.5% water) per pound of dry solids. Since 8.64 pounds of liquid skim milk contain 90.5% water, the remaining 9.5% is dry solids. Therefore, the cost per pound of dry solids would be:
Cost per pound of dry solids = Cost per gallon / Weight of liquid skim milk per gallon * Percentage of dry solids
Cost per pound of dry solids = $1.60 / 8.64 lbs * 9.5% = $0.20
So, the comparative cost of 1lb. dry solids from the liquid milk would be $0.20.