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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 of1.0m×12cm×20cm,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

Expert verified

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

Step by step solution

01

Given data

Dimensions of the filled oyster container are1.0m×12cm×20cm

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

VolumeofContainer=24000cm3=24liters

02

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.

03

Determination of the range

The volume of the container is,

V=1.0m×100cm1m×12cm×20cm=24000cm3

The conversion of pint to liter is as below.

1 pint =0.4732 liter

So,

24liter=24liters×1USpint0.4732liters=50.72U.S.Pints

1U.S.pint=8-12ParcificOysterIf1U.Spint=8parcificOyster.Then,50.72USpints=50.72USpints×8PacificOyster1USPint=405.76ParcificOyster≈406ParcificOyster

If1U.SPint=12PacificOyster,then50.72USpints=5.72USpints×12PacificOyster1USPint=608.64PacificOyster≈609pacificOyster

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

Now, 1pint=26-38AtlanticOyster

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

role="math" localid="1657702043344" 50.72USpints=50.72USpints×26AtlanticOyster1USPint=1318.72AtlanticOyster≈1319AtlanticOyster

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

50.72USpints=50.72USpints×38AtlanticOyster1USPint=1927.36AtlanticOyster≈1927AtlanticOyster

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 give1927-406=1521≈1500and1319-609=710≈700

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

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