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Sarah has whole milk, which contains 
3.25% butterfat by volume, and one type of low-fat milk, which contains 
1% butterfat by volume. Which of the following systems could be used to determine the amount of whole milk, 
w , in ounces, and the amount of low-fat milk, 
l, in ounces, that Sarah should mix to obtain 32 ounces of a low-fat milk with 
2% butterfat by volume?
Choose 1 answer:
(A) 
0.01 l+0.0325 w=32

l+w=0.02
(B) 
0.01 l+0.0325 w=32

l+w=0.64
(c) 
0.01 l+0.0325 w=0.02

l+w=32
(D) 
0.01 l+0.0325 w=0.64

l+w=32

Sarah has whole milk, which contains 3.25%3.25\% butterfat by volume, and one type of low-fat milk, which contains 1%1\% butterfat by volume. Which of the following systems could be used to determine the amount of whole milk, \newlineww, in ounces, and the amount of low-fat milk, ll, in ounces, that Sarah should mix to obtain 3232 ounces of a low-fat milk with 2%2\% butterfat by volume?\newlineChoose 11 answer:\newline(A) 0.01l+0.0325w=320.01 l+0.0325 w=32\newline  \space \space \space \space \space \space \spacel+w=0.02l+w=0.02\newline(B) 0.01l+0.0325w=320.01 l+0.0325 w=32\newline \space \space \space \space \space \space \spacel+w=0.64l+w=0.64\newline(C) 0.01l+0.0325w=0.20.01 l+0.0325 w=0.2\newline  \space \space \space \space \space \space \spacel+w=32l+w=32\newline(D) 0.01l+0.0325w=0.640.01 l+0.0325 w=0.64\newline  \space \space \space \space \space \space \spacel+w=32l+w=32\newline

Full solution

Q. Sarah has whole milk, which contains 3.25%3.25\% butterfat by volume, and one type of low-fat milk, which contains 1%1\% butterfat by volume. Which of the following systems could be used to determine the amount of whole milk, \newlineww, in ounces, and the amount of low-fat milk, ll, in ounces, that Sarah should mix to obtain 3232 ounces of a low-fat milk with 2%2\% butterfat by volume?\newlineChoose 11 answer:\newline(A) 0.01l+0.0325w=320.01 l+0.0325 w=32\newline  \space \space \space \space \space \space \spacel+w=0.02l+w=0.02\newline(B) 0.01l+0.0325w=320.01 l+0.0325 w=32\newline \space \space \space \space \space \space \spacel+w=0.64l+w=0.64\newline(C) 0.01l+0.0325w=0.20.01 l+0.0325 w=0.2\newline  \space \space \space \space \space \space \spacel+w=32l+w=32\newline(D) 0.01l+0.0325w=0.640.01 l+0.0325 w=0.64\newline  \space \space \space \space \space \space \spacel+w=32l+w=32\newline
  1. Identify problem representation: Identify the correct system of equations to represent the problem. We need to find the right combination of whole milk ww and low-fat milk ll to get 3232 ounces of milk with 2%2\% butterfat.
  2. Set up volume equation: Set up the first equation based on the total volume. Since Sarah wants a total of 3232 ounces, the equation is:\newlinel+w=32l + w = 32
  3. Set up butterfat equation: Set up the second equation based on the butterfat content. The total butterfat in the final mixture should be 2%2\% of 3232 ounces, which is 0.640.64 ounces. The equation combining the butterfat contributions from each type of milk is:\newline0.01l+0.0325w=0.640.01l + 0.0325w = 0.64
  4. Match equations to choices: Match the equations to the given choices. The correct system that represents both the total volume and the butterfat content is:\newline0.01l+0.0325w=0.640.01l + 0.0325w = 0.64\newlinel+w=32l + w = 32\newlineThis matches option (D)(D).

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