Question

The corn–hog ratio is a financial term 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 3.108 slugs to the market price of a U.S. bushel of corn. (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 L. If the corn–hog ratio is listed as 5.7 on the market exchange, what is it in the metric units of,

$\frac{\mathrm{price}\mathrm{of}1\mathrm{kilogram}\mathrm{of}\mathrm{pig}}{\mathrm{price}\mathrm{of}1\mathrm{liter}\mathrm{of}\mathrm{corn}}?$

(Hint: See the Mass table in Appendix D.)

Short answer

The Corn-hog ratio in the metric units is$4.4.$

Step-by-step solution

Given data

The corn–hog ratio is the ratio of the market price of a pig with a mass of 3.108 slugs to the market price of a U.S. bushel of corn.

The listed corn-hog ratio is 5.7.

Understanding the unit conversion

Chain-link conversions are used for unit conversion in which given values are multiplied successively by conversion factors.

Converting the given quantities into the required units

Use the conversion factor to convert the quantity in the required unit and find the ratio.

Conversion factor is $1sIug=14.59kg$

Therefore,themass of the pig is,

$$\begin{gathered} 3.108slugs=\left(3.108\right)\left(14.59\right) \\ =45.346kg \end{gathered}$$

The conversion factor is$1Bushel=35.238.$

Determination of the Corn-hog ratio

The Corn hog ratio is given as,$=\frac{\left(priceof3.108slugsofpig\right)}{\left(priceof1Bushelofcorn\right)}$

Substitute the values to calculate the ratio.

$$\begin{gathered} TheCornhogration=\frac{\left(45.346kg\right)}{\left(35.238kg\right)} \\ =5.7 \end{gathered}$$

Multiply the equation by the ratio price of 1 kg of pig and price of 1 liter of corn.

$$\begin{gathered} \frac{\left(45.346\times priceof1kgofpig\right)}{\left(35.238\times priceof1literofcorn\right)}=5.7 \\ 1.287\times \frac{\left(priceof1kgofpig\right)}{\left(priceof1literofcorn\right)}=5.7 \\ \left(\frac{priceof1kgofpig}{priceof1literofcorn}\right)=\frac{5.7}{1.287} \\ =4.4 \end{gathered}$$

Thus, the Corn-hog ratio is 4.4