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Chapter 1: Problem 41

The corn-hog ratio is a financial term commonly used in the pig market and presumably is related to the cost of feeding a pig until it is large enough for market. It is defined as the ratio of the market price of a pig with a mass of 1460 slugs to the market price of a U.S. bushel of corn. The slug is the unit of mass in the English system. (The word "slug" is derived from an old German word that means "to hit"; we have the same meaning for "slug" as a verb in modern English.) A U.S. bushel is equal to \(35.238 \mathrm{~L}\). If the corn-hog ratio is listed as \(5.7\) on the market exchange, what is it in the metric units of \(\frac{\text { price of } 1 \text { kilogram of pig }}{\text { price of } 1 \text { liter of corn }} ?\)

Short Answer

Expert verified
The corn-hog ratio in metric units is approximately 0.1618.

Step by step solution

01

- Understand the Corn-Hog Ratio

The corn-hog ratio is the ratio of the market price of a pig with a mass of 1460 slugs to the market price of a U.S. bushel of corn. It is given as 5.7.
02

- Convert Slugs to Kilograms

1 slug is equal to approximately 14.5939 kilograms. So, the mass of the pig in kilograms is: \[1460 \text { slugs} \times 14.5939 \frac{ \text {kg} }{ \text {slug} } = 21306.094 \text { kg} \]
03

- Convert U.S. Bushels to Liters

1 U.S. bushel is 35.238 liters.
04

- Calculate the Price per Kilogram and per Liter

The corn-hog ratio given is 5.7: \[ \frac{\text { Price of 1460 slugs of pig }}{\text { Price of 1 bushel of corn }} = 5.7 \] Therefore, \[ \frac{\text { Price of 1 kg of pig }}{\text { Price of 35.238 L of corn }} = 5.7 \] Next, let's find the conversion to the price of 1 liter of corn using the ratio:\[ 1 \text { kg of pig } = 5.7 \text { (Price of 35.238 L of corn)} \] Dividing by 35.238 to find the price per liter of corn: \[ 1 \text { kg of pig } = 5.7 \frac{\text{ (Price of 1 liter of corn) }}{35.238} \] Therefore: \[ 1 \text { kg of pig } = 0.1618 \frac{\text { Price of 1 liter of corn }}{1} \]

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Key Concepts

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

Financial Ratios in Agriculture
Financial ratios in agriculture help farmers and market participants understand the economic relationships in farming. One such ratio is the corn-hog ratio.
The corn-hog ratio links the market price of a pig to the market price of a bushel of corn.
This ratio is useful because it signifies the economic viability of raising pigs relative to the cost of their feed.
A high corn-hog ratio indicates it is more profitable to sell pigs than to spend money on corn.
A low ratio could mean the opposite.
Farmers and traders use such financial ratios to make informed decisions about buying, selling, or investing.
They are crucial tools in assessing profitability and market trends.
Keen understanding of these ratios can greatly help in financial planning and strategy.
Unit Conversions
Unit conversions are crucial for solving many practical problems in science and engineering.
In our problem, we need to convert slugs to kilograms and U.S. bushels to liters.
1 slug is approximately 14.5939 kilograms.
Thus, to convert slugs to kilograms, multiply the number of slugs by 14.5939.
Similarly, 1 U.S. bushel equals 35.238 liters. This means that to convert U.S. bushels to liters, you multiply the number of bushels by 35.238.
These conversions help standardize measurements and make calculations easier in the metric system.
Understanding these conversions is essential to solving problems involving different units.
Practical applications can range from cooking recipes to scientific experiments and international trade.
Metric System
The metric system is a decimal-based system of measurement used around the world.
It simplifies calculations by utilizing base units such as meters, kilograms, and liters.
In our problem, converting to metric units involves understanding how much 1 kilogram of pig mass is worth relative to the price of 1 liter of corn.
The decimal nature of the metric system makes it easier to perform such conversions and calculations.
For example, converting from milliliters to liters or grams to kilograms involves simply moving the decimal point.
Many scientific and everyday applications utilize the metric system for its simplicity and universal acceptance.
Grasping metric conversions is foundational for solving various mathematical and real-world problems.
This understanding not only benefits academic pursuits but also practical day-to-day activities.

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Most popular questions from this chapter

An old manuscript reveals that a landowner in the time of King Arthur held \(3.00\) acres of plowed land plus a livestock area of \(25.0\) perches by \(4.00\) perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is 40 perches by 1 perch, and 1 perch is \(16.5 \mathrm{ft}\).

Dose We know from our dimensional analysis that if an object maintains its shape but changes its size, its area changes as the square of its length and its volume changes as the cube of its length. Suppose you are a parent and your child is sick and has to take some medicine. You have taken this medicine previously and you know its dose for you. You are \(5^{\prime} 10^{\prime \prime}\) tall and weigh \(180 \mathrm{lb}\), and your child is \(2^{\prime} 11^{\prime \prime}\) tall and wcighs \(30 \mathrm{lb}\). Estimate an appropriate dosage for your child's medicine in the following cases. Be sure to discuss your reasoning. (a) The medicine is one that will enter the child's bloodstream and reach cvery cell in the body. Your dose is \(250 \mathrm{mg}\). (b) The medicine is one that is meant to coat the child's throat. Your dose is \(15 \mathrm{ml}\).

In the United States, a doll house has the scale of \(1: 12\) of a real house (that is, each length of the doll house is \(\frac{1}{12}\) that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of \(1: 144\) of a real house. Suppose a real house (Fig. \(1-18\) ) has a front length of \(20 \mathrm{~m}\), a depth of \(12 \mathrm{~m}\), a height of \(6.0 \mathrm{~m}\), and a standard sloped roof (vertical triangular faces on the ends) of height \(3.0 \mathrm{~m}\). In cubic meters, what are the volumes of the corresponding (a) doll house and (b) miniature house?

A typical sugar cube has an edge length of \(1 \mathrm{~cm}\). If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole \(=6.02 \times 10^{23}\) units.)

A fortnight is a charming English measure of time equal to \(2.0\) weeks (the word is a contraction of "fourteen nights"). That is a nice amount of time in pleasant company but perhaps a painful string of microseconds in unpleasant company. How many microseconds are in a fortnight?
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