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) 0.01l+0.0325w=32l+w=0.02(B) 0.01l+0.0325w=32l+w=0.64(C) 0.01l+0.0325w=0.2l+w=32(D) 0.01l+0.0325w=0.64l+w=32
Q. 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) 0.01l+0.0325w=32l+w=0.02(B) 0.01l+0.0325w=32l+w=0.64(C) 0.01l+0.0325w=0.2l+w=32(D) 0.01l+0.0325w=0.64l+w=32
Identify problem representation: Identify the correct system of equations to represent the problem. We need to find the right combination of whole milk w and low-fat milk l to get 32 ounces of milk with 2% butterfat.
Set up volume equation: Set up the first equation based on the total volume. Since Sarah wants a total of 32 ounces, the equation is:l+w=32
Set up butterfat equation: Set up the second equation based on the butterfat content. The total butterfat in the final mixture should be 2% of 32 ounces, which is 0.64 ounces. The equation combining the butterfat contributions from each type of milk is:0.01l+0.0325w=0.64
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:0.01l+0.0325w=0.64l+w=32This matches option (D).
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