A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cup of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
A.
7 1/5 cups
B.
2 2/5 cups
C.
3 8/15 cups
D.
6 cups
To determine the amount of milk needed for 2 cups of flour, we first need to find the ratio of flour to milk in the original recipe and then scale it up.
- Convert mixed numbers to improper fractions:
- 13\frac{1}{3}31 cup of flour per 65\frac{6}{5}56 cups of milk.
- Set up the proportion:FlourMilk=2x\frac{\text{Flour}}{\text{Milk}} = \frac{2}{x}MilkFlour=x2where xxx is the amount of milk needed for 2 cups of flour.
- Set up the ratio based on the original recipe:1365=2x\frac{\frac{1}{3}}{\frac{6}{5}} = \frac{2}{x}5631=x2
- Simplify the original ratio:1365=13×56=518\frac{\frac{1}{3}}{\frac{6}{5}} = \frac{1}{3} \times \frac{5}{6} = \frac{5}{18}5631=31×65=185
- Set up the equation with the new amount of flour:518=2x\frac{5}{18} = \frac{2}{x}185=x2
- Solve for xxx by cross-multiplying:5x=365x = 365x=36 x=365=7.2x = \frac{36}{5} = 7.2x=536=7.2To convert 7.27.27.2 into a mixed number:7.2=7210=7157.2 = 7 \frac{2}{10} = 7 \frac{1}{5}7.2=7102=751
Therefore, the amount of milk needed is 7157 \frac{1}{5}751 cups.
The correct answer is:
A. 7 1/5 cups