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
To find out how much milk is needed for 3 cups of flour, we need to use the given ratio of flour to milk and scale it up accordingly.
The recipe ratio is: 5/7 cup of flour235 cups of milk\frac{5/7 \text{ cup of flour}}{2 \frac{3}{5} \text{ cups of milk}}253 cups of milk5/7 cup of flour
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: 5/713/5\frac{5/7}{13/5}13/55/7
To find out how much milk is needed for 3 cups of flour, set up a proportion: 5/713/5=3x\frac{5/7}{13/5} = \frac{3}{x}13/55/7=x3
Solve for xxx (the amount of milk needed): 5/713/5=3x\frac{5/7}{13/5} = \frac{3}{x}13/55/7=x3
Cross-multiply to solve for xxx: 57×513=3x\frac{5}{7} \times \frac{5}{13} = \frac{3}{x}75×135=x3 2591=3x\frac{25}{91} = \frac{3}{x}9125=x3
Cross-multiply to solve for xxx: 25x=27325x = 27325x=273 x=27325x = \frac{273}{25}x=25273 x=10.92 (approximately)x = 10.92 \text{ (approximately)}x=10.92 (approximately)
Convert this to a mixed number: 10.92=10232510.92 = 10 \frac{23}{25}10.92=102523
So, the amount of milk needed is:
D. 10 23/25 cups