A recipe calls for 5/7 cup of flour for every 2 3/5 cup of milk. To make a bigger batch, the chef uses 3 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
A.
12 1/5 cups
B.
12 2/5 cups
C.
8 9/25 cups
D.
10 23/25 cups
The Correct Answer and Explanation is:
To determine how much milk is needed when using 3 cups of flour, given the original ratio in the recipe, we need to follow these steps:
- Understand the Original Ratio: The recipe specifies a ratio of 57\frac{5}{7}75 cup of flour for every 2352 \frac{3}{5}253 cups of milk. First, convert 2352 \frac{3}{5}253 to an improper fraction:235=10+35=1352 \frac{3}{5} = \frac{10 + 3}{5} = \frac{13}{5}253=510+3=513So, the ratio is 57\frac{5}{7}75 cup of flour to 135\frac{13}{5}513 cups of milk.
- Set Up the Proportion: Let xxx represent the amount of milk needed for 3 cups of flour. Using the original ratio:57135=3x\frac{\frac{5}{7}}{\frac{13}{5}} = \frac{3}{x}51375=x3We solve this proportion to find xxx.
- Solve the Proportion: Start by simplifying the left side of the proportion:57135=57×513=2591\frac{\frac{5}{7}}{\frac{13}{5}} = \frac{5}{7} \times \frac{5}{13} = \frac{25}{91}51375=75×135=9125So the proportion is:2591=3x\frac{25}{91} = \frac{3}{x}9125=x3To solve for xxx, cross-multiply and solve:25x=91×325x = 91 \times 325x=91×3 25x=27325x = 27325x=273 x=27325=10.92x = \frac{273}{25} = 10.92x=25273=10.92
- Convert the Result: The decimal 10.92 can be converted to a mixed number. 0.920.920.92 is approximately 2325\frac{23}{25}2523. Therefore, 10.9210.9210.92 is 10232510 \frac{23}{25}102523.
- Match to the Given Options: Among the given options:
- A. 121512 \frac{1}{5}1251 cups
- B. 122512 \frac{2}{5}1252 cups
- C. 89258 \frac{9}{25}8259 cups
- D. 10232510 \frac{23}{25}102523 cups
Thus, the correct amount of milk needed for the bigger batch is 10232510 \frac{23}{25}102523 cups, which corresponds to option D.
This approach ensures accuracy by first converting mixed numbers to improper fractions, setting up a proportion, and then solving it step by step to find the precise amount of milk needed.