An old English cookbook carries this recipe for cream of nettle soup: “Boil stock of the following amount: 1 breakfastcup plus 1 teacup plus 6 tablespoons plus 1 dessertspoon. Using gloves, separate nettle tops until you have 0.5 quart; add the tops to the boiling stock. Add 1 tablespoon of cooked rice and 1 saltspoon of salt. Simmer for 15 min.” The following table gives some of the conversions among old (premetric) British measures and among common (still premetric) U.S. measures. (These measures just scream for metrication.) For liquid measures, 1 British teaspoon = 1 U.S. teaspoon. For dry measures, 1 British teaspoon = 2 U.S. teaspoons and 1 British quart =1 U.S. quart. In U.S. measures, how much (a) stock, (b) nettle tops, (c) rice, and (d) salt are required in the recipe?

Old British Measures	U.S. Measures
teaspoon = 2 saltspoons	tablespoon = 3 teaspoons
dessertspoon = 2 teaspoons	half cup = 8 tablespoons
tablespoon = 2 dessertspoons	cup = 2 half cups
teacup = 8 tablespoons
breakfastcup = 2 teacups

For dry measures,

1 British teaspoon = 2 U.S teaspoon

1 British quart = 1 U.S quart

For liquid measures,

1 British teaspoon = 1 U.S teaspoon

The conversion factors can be used to convert the physical quantity from one unit to another unit. Using the given conversion factors, find the amount of stock, rice, nettle tops, and salt required in the recipe.

The amount of stock required in the recipe is,

$$\begin{gathered} \mathrm{Amount}\mathrm{of}\mathrm{stock}=1\mathrm{breakfast}\mathrm{cup}+1\mathrm{teacup}+6\mathrm{tablespoons}+1\mathrm{dessert}\mathrm{spoon}...\left(\mathrm{i}\right) \\ 1\mathrm{breakfast}\mathrm{cup}=2\mathrm{tea}\mathrm{cup}\times 8\mathrm{table}\mathrm{spoons}\times 2\mathrm{dessert}\mathrm{spoon}\times 2\mathrm{tea}\mathrm{spoon} \\ 1\mathrm{tea}\mathrm{cup}=8\mathrm{table}\mathrm{spoons}\times 2\mathrm{dessert}\mathrm{spoon}\times 2\mathrm{tea}\mathrm{spoon} \\ 6\mathrm{tablespoons}=2\mathrm{dessert}\mathrm{spoon}\times 2\mathrm{tea}\mathrm{spoon} \\ 1\mathrm{dessert}\mathrm{spoon}=2\mathrm{tea}\mathrm{spoon} \end{gathered}$$

Substituting the all above quantities in equation (i).

$$\begin{gathered} \mathrm{Amount}\mathrm{of}\mathrm{stock}=\left[\left(2\right)\left(8\right)\left(2\right)\left(2\right)+\left(8\right)\left(2\right)\left(2\right)+6\left(2\right)\left(2\right)+1\left(2\right)\right] \\ =122\mathrm{U}.\mathrm{S}.\mathrm{teaspoons} \end{gathered}$$

Thus, the amount of stock is $122\mathrm{U}.\mathrm{S}.\mathrm{teaspoons}.$

The amount of nettle tops required in the recipe is,

$0.5\mathrm{British}\mathrm{quart}=0.5\mathrm{U}.\mathrm{S}\mathrm{quart}.$

The amount of rice required in the recipe is

$$\begin{gathered} 1tablespoon=2dessertspoons=4taspoons \\ 1U.Steaspoons=1Britishteaspoon \\ 1tablespoon=4teaspoon \end{gathered}$$

Thus, the amount of rice required is $4\mathrm{U}.\mathrm{S}.\mathrm{teaspoon}$.

The amount of salt required in the recipe is,

$1\mathrm{saltspoon}=\frac{1}{2}\mathrm{teaspoon}.$

Thus, the amount of salt required is $\frac{1}{2}\mathrm{U}.\mathrm{S}.\mathrm{teaspoon}.$