Question

In purchasing food for a political rally, you erroneously order shucked medium-size Pacific oysters (which come 8 to 12 per U.S. pint) instead of shucked medium-size Atlantic oysters (which come 26 to 38 per U.S. pint). The filled oyster container shipped to you has the interior measure of$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{m}\mathbf{\times }\mathbf{12}\mathbf{cm}\mathbf{\times }\mathbf{20}\mathbf{cm}$,and a U.S. pint is equivalent to 0.4732 liter . By how many oysters is the order short of your anticipated count?

Short answer

The order is roughly short of 700-1500 oysters from the anticipated count

Step-by-step solution

Given data

Dimensions of the filled oyster container are$1.0\mathrm{m}\times 12\mathrm{cm}\times 20\mathrm{cm}$

One U.S. pint is equivalent to 0.4732 liter.

$\mathrm{Volume}\mathrm{of}\mathrm{Container}=24000{\mathrm{cm}}^3=24\mathrm{liters}$

Conversion of quantities into required units.

To find the range of shortage, take the difference between the smallest value from the first range and the largest value from the second and then the difference between the largest value from the first range and the smallest value of the second range.

Determination of the range

The volume of the container is,

$$\begin{gathered} \mathrm{V}=\left(1.0\mathrm{m}\times \frac{100\mathrm{cm}}{1\mathrm{m}}\right)\times 12\mathrm{cm}\times 20\mathrm{cm} \\ =24000{\mathrm{cm}}^3 \end{gathered}$$

The conversion of pint to liter is as below.

1 pint =0.4732 liter

So,

$$\begin{gathered} 24\mathrm{liter}=24\mathrm{liters}\times \frac{1\mathrm{US}\mathrm{pint}}{0.4732\mathrm{liters}} \\ =50.72\mathrm{U}.\mathrm{S}.\mathrm{Pints} \end{gathered}$$

$$\begin{gathered} 1\mathrm{U}.\mathrm{S}.\mathrm{pint}=8-12\mathrm{Parcific}\mathrm{Oyster} \\ \mathrm{If}1\mathrm{U}.\mathrm{S}\mathrm{pint}=8\mathrm{parcific}\mathrm{Oyster}.\mathrm{Then}, \\ 50.72\mathrm{US}\mathrm{pints}=50.72\mathrm{US}\mathrm{pints}\times \frac{8\mathrm{Pacific}\mathrm{Oyster}}{1\mathrm{US}\mathrm{Pint}} \\ =405.76\mathrm{Parcific}\mathrm{Oyster} \\ \approx 406\mathrm{Parcific}\mathrm{Oyster} \end{gathered}$$

$$\begin{gathered} \mathrm{If}1\mathrm{U}.\mathrm{S}\mathrm{Pint}=12\mathrm{Pacific}\mathrm{Oyster},\mathrm{then} \\ 50.72\mathrm{US}\mathrm{pints}=5.72\mathrm{US}\mathrm{pints}\times \frac{12\mathrm{Pacific}\mathrm{Oyster}}{1\mathrm{US}\mathrm{Pint}} \\ =608.64\mathrm{Pacific}\mathrm{Oyster} \\ \approx 609\mathrm{pacific}\mathrm{Oyster} \end{gathered}$$

So, range of the pacific oyster is 406-609 .

Now, $1\mathrm{pint}=26-38\mathrm{Atlantic}\mathrm{Oyster}$

If 1 U.S pint=26 Atlantic Oyster,then,

role="math" localid="1657702043344" $$\begin{gathered} 50.72\mathrm{US}\mathrm{pints}=50.72\mathrm{US}\mathrm{pints}\times \frac{26\mathrm{Atlantic}\mathrm{Oyster}}{1\mathrm{US}\mathrm{Pint}} \\ =1318.72\mathrm{Atlantic}\mathrm{Oyster} \\ \approx 1319\mathrm{Atlantic}\mathrm{Oyster} \end{gathered}$$

If 1 U.S pint=38 Atlantic Oyster , then,

$$\begin{gathered} 50.72\mathrm{US}\mathrm{pints}=50.72\mathrm{US}\mathrm{pints}\times \frac{38\mathrm{Atlantic}\mathrm{Oyster}}{1\mathrm{US}\mathrm{Pint}} \\ =1927.36\mathrm{Atlantic}\mathrm{Oyster} \\ \approx 1927\mathrm{Atlantic}\mathrm{Oyster} \end{gathered}$$

So, range of the Atlantic Oyster is $1319-1927$.

To find the range of shortage, take the differencebetween the smallestvaluefrom the firstrange and the largest value from the second and then the differencebetween the largestvalue from the first range and the smallest value of the second range.

This would give$\left(1927-406=1521\approx 1500\right)\mathrm{and}\left(1319-609=710\approx 700\right)$

Thus, the shortage of the oyster would be in the range of (700-1500) .