Question

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?
○ \\(\frac{1}{5}\\) cup
○ \\(\frac{1}{4}\\) cup
○ \\(\frac{3}{4}\\) cup
○ \\(\frac{4}{5}\\) cup

Explanation:

Step1: Define variables

Let \( x \) be the volume of cream (in cups), then the volume of milk is \( 1 - x \) cups.

Step2: Set up fat equation

The fat from cream is \( 0.18x \), fat from milk is \( 0.02(1 - x) \), and fat in mixture is \( 0.06(1) \). So:
\( 0.18x + 0.02(1 - x) = 0.06(1) \)

Step3: Simplify equation

Expand: \( 0.18x + 0.02 - 0.02x = 0.06 \)
Combine like terms: \( 0.16x + 0.02 = 0.06 \)
Subtract 0.02: \( 0.16x = 0.04 \)

Step4: Solve for \( x \)

Divide by 0.16: \( x = \frac{0.04}{0.16} = \frac{1}{4} \)? Wait, no, wait: \( 0.04\div0.16 = \frac{4}{16} = \frac{1}{4} \)? Wait, no, 0.04 is 4/100, 0.16 is 16/100, so \( \frac{4}{100}\div\frac{16}{100} = \frac{4}{16} = \frac{1}{4} \)? Wait, but let's check again. Wait, the equation:

\( 0.18x + 0.02(1 - x) = 0.06 \)

\( 0.18x + 0.02 - 0.02x = 0.06 \)

\( 0.16x = 0.06 - 0.02 = 0.04 \)

\( x = 0.04 / 0.16 = 0.25 = 1/4 \)? Wait, but let's verify. If cream is 1/4 cup (0.25), milk is 3/4 cup (0.75). Fat from cream: 0.180.25 = 0.045, fat from milk: 0.020.75 = 0.015. Total fat: 0.045 + 0.015 = 0.06, which is 6% of 1 cup (0.06). Yes, that works. Wait, but the options have 1/4 cup as an option. Wait, but let me check my calculation again. Wait, 0.18x + 0.02(1 - x) = 0.06*1.

0.18x + 0.02 - 0.02x = 0.06

0.16x = 0.04

x = 0.04 / 0.16 = 1/4. So the volume of cream is 1/4 cup? Wait, but let's see the options. The first option is 1/5, then 1/4. Wait, maybe I made a mistake. Wait, no, 0.04 divided by 0.16 is 0.25, which is 1/4. So the answer should be 1/4 cup. Wait, but let's check again.

Wait, fat from cream: 1/4 cup 18% = 0.25 0.18 = 0.045

Fat from milk: 3/4 cup 2% = 0.75 0.02 = 0.015

Total fat: 0.045 + 0.015 = 0.06, which is 6% of 1 cup. So that's correct. So the volume of cream is 1/4 cup.

Wait, but the options are 1/5, 1/4, 3/4, 4/5. So 1/4 is an option. So the correct answer is 1/4 cup.

Answer:

\(\boldsymbol{\frac{1}{4}}\) cup (Option: \(\frac{1}{4}\) cup)