A macaroni and cheese recipe calls for 1/4 cup of flour for every 1 1/6 cup of milk. To make a bigger batch, the chef uses 5 cups of flour.
Which of the following would be the amount of milk needed for the bigger batch?
A.
21 3/5 cups
B.
20 1/3cups
C.
23 4/9 cups
D.
23 1/3 cups
The Correct answer and Explanation is:
To solve this problem, we need to determine the amount of milk required when using 5 cups of flour, based on the given ratio in the macaroni and cheese recipe. The recipe states that for every 1/4 cup of flour, 1 1/6 cups of milk are needed.
Step 1: Determine the ratio of flour to milk.
The original ratio of flour to milk is:1/4 cup of flour116 cups of milk=1/47/6\frac{1/4 \text{ cup of flour}}{1 \frac{1}{6} \text{ cups of milk}} = \frac{1/4}{7/6} 161 cups of milk1/4 cup of flour=7/61/4
Step 2: Simplify the ratio.
To simplify 1/47/6\frac{1/4}{7/6}7/61/4, we multiply by the reciprocal of the denominator:1/47/6=1/4×6/71=628=314\frac{1/4}{7/6} = \frac{1/4 \times 6/7}{1} = \frac{6}{28} = \frac{3}{14}7/61/4=11/4×6/7=286=143
Thus, for every 3 units of milk, 14 units of flour are required.
Step 3: Set up a proportion for the larger batch.
Let xxx represent the amount of milk needed for 5 cups of flour. Set up the proportion:1/4116=5x\frac{1/4}{1 \frac{1}{6}} = \frac{5}{x} 1611/4=x5
Step 4: Solve for xxx.
To cross-multiply and solve for xxx, calculate:51×14/3=x\frac{5}{1} \times 14/3 = x 15×14/3=x
Solving the above provides the exact correct response value.