scenario 5: you have been asked to cater a dinner for 6 people. the host has asked you to make your famous…

scenario 5: you have been asked to cater a dinner for 6 people. the host has asked you to make your famous chocolate cake for dessert. the only problem with that is your chocolate cake recipe has a yield of 12 servings. new yield = \n\nold yield = \n\nrcf = 0.5\n\ningredients rcf new totals\n4 c cake flour 4×0.5 2\n2 c cocoa powder 2×0.5 1\n2 1/4 c sugar 2 1/4×0.5 \n2 t baking powder 2×0.5 \n1 t baking soda 1×0.5 \n1 t salt 1×0.5 \n4 eggs 4×0.5 \n2 t vanilla extract 2×0.5 \n1 1/3 c milk 1 1/3×0.5 \n2 1/2 c oil 2 1/2×0.5 \n3 c hot coffee 3×0.5

scenario 5: you have been asked to cater a dinner for 6 people. the host has asked you to make your famous chocolate cake for dessert. the only problem with that is your chocolate cake recipe has a yield of 12 servings. new yield = \n\nold yield = \n\nrcf = 0.5\n\ningredients rcf new totals\n4 c cake flour 4×0.5 2\n2 c cocoa powder 2×0.5 1\n2 1/4 c sugar 2 1/4×0.5 \n2 t baking powder 2×0.5 \n1 t baking soda 1×0.5 \n1 t salt 1×0.5 \n4 eggs 4×0.5 \n2 t vanilla extract 2×0.5 \n1 1/3 c milk 1 1/3×0.5 \n2 1/2 c oil 2 1/2×0.5 \n3 c hot coffee 3×0.5

Answer

Explanation:

Step1: Calculate the Recipe Conversion Factor (RCF)

The formula for RCF is $\frac{\text{New Yield}}{\text{Old Yield}}$. Here, the new yield is for 6 people and the old yield is 12 servings. So, $RCF=\frac{6}{12}= 0.5$.

Step2: Calculate new ingredient amounts

For each ingredient, multiply the original amount by the RCF.

  • Cake Flour: Original amount is 4 C. New amount is $4\times0.5 = 2$ C.
  • Cocoa Powder: Original amount is 2 C. New amount is $2\times0.5=1$ C.
  • Sugar: Original amount is $2\frac{1}{4}$ C. First convert $2\frac{1}{4}=\frac{9}{4}$ C. New amount is $\frac{9}{4}\times0.5=\frac{9}{4}\times\frac{1}{2}=\frac{9}{8} = 1\frac{1}{8}$ C.
  • Baking Powder: Original amount is 2 t. New amount is $2\times0.5 = 1$ t.
  • Baking Soda: Original amount is 1 t. New amount is $1\times0.5=0.5$ t.
  • Salt: Original amount is 1 T. New amount is $1\times0.5 = 0.5$ T.
  • Eggs: Original amount is 4. New amount is $4\times0.5 = 2$.
  • Vanilla Extract: Original amount is 2 T. New amount is $2\times0.5 = 1$ T.
  • Milk: Original amount is $1\frac{1}{3}$ C. Convert $1\frac{1}{3}=\frac{4}{3}$ C. New amount is $\frac{4}{3}\times0.5=\frac{4}{3}\times\frac{1}{2}=\frac{2}{3}$ C.
  • Oil: Original amount is $2\frac{1}{2}$ C. Convert $2\frac{1}{2}=\frac{5}{2}$ C. New amount is $\frac{5}{2}\times0.5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4}=1\frac{1}{4}$ C.
  • Hot Coffee: Original amount is 3 C. New amount is $3\times0.5 = 1.5$ C.

Answer:

Ingredients New totals
4 C Cake Flour 2 C
2 C Cocoa Powder 1 C
$2\frac{1}{4}$ C Sugar $1\frac{1}{8}$ C
2 t Baking Powder 1 t
1 t Baking Soda 0.5 t
1 T Salt 0.5 T
4 Eggs 2
2 T Vanilla Extract 1 T
$1\frac{1}{3}$ C Milk $\frac{2}{3}$ C
$2\frac{1}{2}$ C Oil $1\frac{1}{4}$ C
3 C Hot Coffee 1.5 C