2 pounds fresh asparagus, trimmed and cut into 1 inch pieces
1 cup chopped onion
1 quart chicken stock
4 tablespoons butter
4 tablespoons all-purpose flour
2 teaspoon salt
2 pinch ground black pepper
2 cup milk
1 cup sour cream
2 teaspoon fresh lemon juice
Question: Is there an easy way to figure out how much of each ingredient we need to purchase for the event?
The Answer is...
What Grumpy Cat Means to Say is...
YES! Just remember the three NOs!
NO #1: To scale up the recipe to $53$ guests, we construct a recipe conversion factor, or $RCF$, by dividing the $N$ew Recipe Yield by the $O$ld recipe Yield. That is, $$RCF=\frac{N}{O}$$
NO #1 Example: For the soup recipe given above, the $O$ld yield enough to serve $8$ people, and the $N$ew yield should be enough to serve $53$ people. Therefore $$RCF=\frac{N}{O}=\frac{53 \mbox{ guests}}{8 \mbox{ guests}}=\frac{53}{8}=6.625$$ Fact: The $RCF$ is the number we must multiply all quantities in our by in order to scale the recipe up or down. Thus, for example, the amount of asparagus we need to serve $53$ guests is $2 \mbox{ lb} \times 6.625=13.25 \mbox{ lb}.$
NO #2: NO Rounding the $RCF!$
We saw that $$RCF=\frac{N}{O}=\frac{53 \mbox{ guests}}{8 \mbox{ guests}}=\frac{53}{8}=6.625$$ and we didn't round. In fact, we never round. We simply leave it as is.
NO #3: NO Units!
Again, $$RCF=\frac{N}{O}=\frac{53 \mbox{ guests}}{8 \mbox{ guests}}=\frac{53}{8}=6.625$$ Notice the $N$ and the $O$ in the above have THE SAME UNITS, both of which cancel.
This means that the $RCF$ is a unitless quantity. NO units!
Dire Warning! Stop Taking Notes! Do not mix up $N$ and $O!$
It is a common mistake for students to use the incorrect (don't write this down!) formula $$RCF=\frac{O}{N}$$ This is wrong.
Remember the answer is NO! NO! NO!
Example: Today Billy Bob needs to make $2.75$ gallons of his Spicy Cajun Cioppino for a hootenanny he's catering. However, his original recipe makes only makes $1.5$ gallons of cioppino. His secret recipe calls for $14\frac{1}{2}$ fluid ounces of chicken broth. How much broth is Billy Bob going to need for the hootenanny?
Bonus Example: For the hootenanny Billy Bob is catering, there needs to be a non-spicy option. By special request, he is making his regionally acclaimed Shotgun Wedding Stew. The guests want $70$ portions which are $6$ fluid ounces each. However, his original recipe makes $55$ portions which are $10$ fluid ounces each.
Billy Bob's original (and very secret!) recipe calls for $2.5$ pounds of deer sausage. How much sausage should Billy Bob add to the stew which he is serving at the hootenanny? Round your answer to the nearest hundredth.