milk and cream are mixed together for a recipe. the total volume of the mixture is 1 cup. if the milk…

milk and cream are mixed together for a recipe. the total volume of the mixture is 1 cup. if the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?\no $\frac{1}{5}$ cup\no $\frac{1}{4}$ cup\no $\frac{3}{4}$ cup\no $\frac{4}{5}$ cup

milk and cream are mixed together for a recipe. the total volume of the mixture is 1 cup. if the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?\no $\frac{1}{5}$ cup\no $\frac{1}{4}$ cup\no $\frac{3}{4}$ cup\no $\frac{4}{5}$ cup

Answer

Explanation:

Step1: Let the volume of cream be $x$ cups.

Since the total volume is 1 cup, the volume of milk is $(1 - x)$ cups.

Step2: Set up an equation based on fat - content.

The fat - content in milk is $0.02(1 - x)$ (because 2% = 0.02), the fat - content in cream is $0.18x$ (because 18% = 0.18), and the fat - content in the mixture is $0.06\times1$ (because 6% = 0.06 and total volume is 1 cup). So the equation is $0.02(1 - x)+0.18x=0.06\times1$.

Step3: Expand and simplify the equation.

$0.02-0.02x + 0.18x=0.06$. Combine like terms: $0.02+(0.18x - 0.02x)=0.06$, which gives $0.02 + 0.16x=0.06$.

Step4: Solve for $x$.

Subtract 0.02 from both sides: $0.16x=0.06 - 0.02$, so $0.16x=0.04$. Then divide both sides by 0.16: $x=\frac{0.04}{0.16}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$ cup