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Chapter 1: Problem 37

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 delivered to you has the interior measure of \(1.0 \mathrm{~m} \times 12 \mathrm{~cm} \times 20 \mathrm{~cm}\), 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

Expert verified
The order is 1115 oysters short.

Step by step solution

01

- Calculate the volume of the container in liters

First, convert the dimensions of the container from meters and centimeters to liters. Since 1 meter = 100 centimeters, the dimensions are Interior measure: Length = 1.0 m Width = 12 cm Height = 20 cm Convert everything to centimeters: 1.0 m = 100 cm Thus, the volume in cubic centimeters is: Volume = Length 脳 Width 脳 Height = 100 cm 脳 12 cm 脳 20 cm = 24000 cm鲁 Knowing that 1 liter = 1000 cm鲁, convert the volume to liters: Volume = 24000 cm鲁 梅 1000 = 24 liters
02

- Convert the volume of the container to U.S. pints

Since 1 U.S. pint = 0.4732 liters, convert the volume of the container from liters to U.S. pints: Volume in pints = Volume in liters 梅 0.4732 Volume in pints = 24 liters 梅 0.4732 = 50.7 pints
03

- Calculate the number of Pacific oysters in the container

Pacific oysters come 8 to 12 per U.S. pint. Calculate the average number of Pacific oysters per pint: Average = (8 + 12) 梅 2 = 10 oysters per pint So, the total number of Pacific oysters in the container is: Number of Pacific oysters = Volume in pints 脳 Average number of Pacific oysters per pint = 50.7 pints 脳 10 oysters per pint = 507 oysters
04

- Calculae the number of anticipated Atlantic oysters

Atlantic oysters come 26 to 38 per U.S. pint. Calculate the average number of Atlantic oysters per pint: Average = (26 + 38) 梅 2 = 32 oysters per pint So, the total number of anticipated Atlantic oysters in the container is: Number of Atlantic oysters = Volume in pints 脳 Average number of Atlantic oysters per pint = 50.7 pints 脳 32 oysters per pint = 1622.4 oysters
05

- Calculate the deficit of oysters

Subtract the actual number of Pacific oysters from the anticipated number of Atlantic oysters in the container: Deficit = Number of Atlantic oysters - Number of Pacific oysters = 1622.4 oysters - 507 oysters = 1115.4 oysters Since we can't have a fraction of an oyster, round to the nearest whole number: Deficit 鈮� 1115 oysters

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Conversion
When you solve problems in physics involving volume calculation, accurate unit conversion is crucial. In this exercise, we start by converting all measurements to the same units. We have a container with mixed units: length in meters and width and height in centimeters. First, we need to convert all dimensions to centimeters because it's simpler to calculate this way. Remember, 1 meter = 100 centimeters, so 1.0 meter becomes 100 centimeters.
Then you calculate the volume in cubic centimeters (cm鲁). Once you have it, you convert cubic centimeters to liters since 1 liter = 1000 cm鲁. In our case, we get 24 liters.
Finally, convert liters to U.S. pints, knowing 1 U.S. pint is equivalent to 0.4732 liters. This process ensures you're working with manageable numbers, making it easier to understand and solve the problem.
Volume Measurement
Measuring volume accurately is fundamental in understanding how much space an object (or in this case, oysters) occupies. To measure volume, multiply the container's length, width, and height. Given measurements are 1.0 m (which converts to 100 cm), 12 cm, and 20 cm.
So, the volume calculation goes: Volume = Length 脳 Width 脳 Height = 100 cm 脳 12 cm 脳 20 cm = 24000 cm鲁.
To convert this to liters, divide by 1000, leading to a calculated volume of 24 liters.
To convert this to U.S. pints (a standard unit for describing volumes of liquids in the U.S.), you divide the volume in liters by the conversion factor 0.4732, enabling you to express the volume in pints鈥� a common practical step in volume measurement when dealing with real-world problems.
Problem-Solving Steps
Let's break down the steps taken to solve this volume-related problem. Each step focuses on converting and calculating accurately.
First: Calculate the volume of the container in a more useful unit like liters, starting from provided dimensions.
Second: Convert the container's volume from liters to U.S. pints to match the units for oysters per pint.
Third: Determine the number of Pacific oysters in the container. Calculate the average number of oysters per pint (for Pacific oysters, 8 to 12 per pint, averaging at 10) and multiply this average by the total volume in pints (50.7 pints). This gives the total Pacific oysters: 507.
Fourth: Find the expected number of Atlantic oysters. Like before, use the average oysters per pint (26 to 38 per pint, averaging at 32) and multiply this by the total pints (50.7 pints). This results in approximately 1622.4 Atlantic oysters.
Fifth: Subtract the actual number of Pacific oysters from the expected Atlantic oysters to find the deficit (1622.4 - 507 oysters = 1115.4 oysters). Round to the nearest whole number, resulting in about 1115 oysters short.
This structured approach exemplifies how breaking down complex problems into simpler tasks can make solution finding more approachable and accurate.

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Most popular questions from this chapter

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