A recipe calls for 5/7 cup of flour for every 2 3/5 cup of milk.

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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:

  1. 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​=513​So, the ratio is 57\frac{5}{7}75​ cup of flour to 135\frac{13}{5}513​ cups of milk.
  2. 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}513​75​​=x3​We solve this proportion to find xxx.
  3. 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}513​75​​=75​×135​=9125​So the proportion is:2591=3x\frac{25}{91} = \frac{3}{x}9125​=x3​To 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
  4. 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​.
  5. 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
    The closest match to 10232510 \frac{23}{25}102523​ cups is option D.

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.

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