Question

Prof. Glatt likes 2% milk (2% fat) for her cereal in the morning. Her parents only buy wholemilk (3.5% fat) and non-fat milk (0% fat). While she is visiting her parents, how much of eachtype of milk does she need to mix to get 3 cups of 2% milk. The answer can be rounded to thenearest tenth.linear systems solving algebraically

Answer 1

It is given that there are two types of milk.

One is 3.5% and one is 0%.

Let the number of cups of 3.5% milk be x and the number of cups of 0% milk used be y.

The total should be 3 cups so it follows:

`x+y=3\ldots(i)`

It is also known that the resulting milk is 2% so it follows:

`\begin{gathered} (3.5)/(100)x+(0)/(100)y=(2)/(100)(x+y) \\ (3.5)/(100)x=(2)/(100)(x+y) \end{gathered}`

Multiply by 100 on both sides to get:

`\begin{gathered} 3.5x=2(x+y) \\ 3.5x=2x+2y \\ 1.5x=2y \\ x=(2)/(1.5)y \\ x=(2*2)/(1.5*2)y \\ x=(4)/(3)y \end{gathered}`

Substitute the value of (ii) in (i) to get:

`\begin{gathered} x+y=3 \\ (4)/(3)y+y=3 \\ (4+3)/(3)y=3 \\ (7)/(3)y=3 \\ (3)/(7)*(7)/(3)y=(3)/(7)*3 \\ y=(9)/(7) \end{gathered}`

Hence the quantity of 0% milk is 9/7 cups.

The quantity of 3.5% milk is given by:

`\begin{gathered} x=(4)/(3)y \\ x=(4)/(3)*(9)/(7) \\ x=(12)/(7) \end{gathered}`

Hence the quantity of 3.5% milk is 12/7 cups.