Open in App
Log In Start studying!

Select your language

Suggested languages for you:

Problem 470

A rancher sold 25 hogs and 60 sheep to Mr. Kay for \(\$ 3450 .\) At the same prices, he sold 35 hogs and 50 sheep to Mr. Bea for \(\$ 3300\). Find the price of each hog and sheep.

Short Answer

Expert verified
Thus, the price of each hog is \$30 and the price of each sheep is \$45.
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Over 22 million students worldwide already upgrade their learning with Vaia!

Step 1: Create the system of linear equations

We are given the total number of hogs and sheep bought by Mr. Kay and Mr. Bea along with their respective payments. Let's represent the price of each hog by x and the price of each sheep by y. Then we can create the following equations based on the provided information: 1. \( 25x + 60y = 3450 \) (Total payment by Mr. Kay) 2. \( 35x + 50y = 3300 \) (Total payment by Mr. Bea) These are our two linear equations.

Step 2: Solve the system of linear equations

Now, let's solve these equations to find the values of x and y, which represent the prices of hogs and sheep. There are several methods to solve a system of linear equations, like substitution, elimination, and matrix method. Here, we will use the elimination method. First, multiply equation (1) by 7 and equation (2) by 5 to make the coefficients of x equal: 1. \( 175x + 420y = 24150 \) (Multiplying equation 1 by 7) 2. \( 175x + 250y = 16500 \) (Multiplying equation 2 by 5) Now, subtract equation (2) from equation (1): \( 170y = 7650 \) Next, divide by 170 on both sides to get the value of y: \( y = 45 \) (Price of each sheep) Now that we have found the price of each sheep, we can find the price of each hog by substituting the value of y in either of the equations. We will substitute it in equation (1): \( 25x + 60(45) = 3450 \) Simplify the equation: \( 25x + 2700 = 3450 \) Subtract 2700 from both sides: \( 25x = 750 \) Finally, divide by 25 on both sides to get the value of x: \( x = 30 \) (Price of each hog)

Step 3: Write the final answer

So, the price of each hog is \$30 and the price of each sheep is \$45.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 19

Suppose that two costume companies each make clown, skeleton, and space costumes. They all sell for the same amount and use the same machinery and workmanship. Furthermore, the market for costumes is fixed; a certain given number of total costumes will be sold this Halloween. But each company has its own individual styles which affect how the costumes sell. On the basis of past experience, the following matrix has been inferred. It indicates, for example, that if both make clown outfits, then for every 20 that are sold, company I will lose 2 sales to company II. Similarly, if company I makes clown outfits and company II makes space suits, then for each 20 sold, company I will sell 4 more than company II.

Chapter 19

Consider a buyer who at the beginning of each month decides whether to buy brand 1 or brand 2 that month. Each month the buyer will select either brand 1 or 2 . The selection he makes at the beginning of any one month depends at most on the selection he made in the immediately preceding month and not on any other previous selections. Let \(\mathrm{p}_{\mathrm{ij}}\) denote the probability that at the beginning of any month the buyer selects brand \(j\) given that he bought brand i the preceding month. Suppose we know that \(p_{11}=3 / 4, p_{12}=1 / 4\), \(\mathrm{p}_{21}=1 / 2\) and $\mathrm{p}_{22}=1 / 2$ 1) First draw the transition diagram. 2) Assuming that the first month under consideration is January, determine the distribution of probabilities for April.

Chapter 19

The technique used to estimate a relationship of the form \(\mathrm{Y}=\beta_{0}+\beta \mathrm{X}\) is known as simple regression. Generalize this technique to estimate a relationship of the form, $$ \mathrm{Y}=\beta_{0}+\beta_{1} \mathrm{X}_{1}+\beta_{2} \mathrm{X}_{2}+\ldots+\beta_{\mathrm{K}} \mathrm{X}_{\mathrm{K}} $$ where \(\mathrm{K}\) is some positive integer. This new technique is known as multiple regression.

Chapter 19

1) Show that the standard deviation of \(\mathrm{X}\) and \(\mathrm{Y}\) corresponds to vector addition (according to the parallelogram law). 2) Solve the following problems: (a) Suppose that 3 resistors are placed in series. The standard deviations of the given resistances are 20,20 and 10 ohms, respectively. What is the standard deviation of the resistance of the series combination? (b) Gears \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}^{\prime}\) s widths have standard deviations of \(0.001,0.004\), and \(.002\) in., respectively. If these are assembled side by side on a single shaft what is the standard deviation of this total width?

Chapter 19

A highly specialized industry builds one device each month. The total monthly demand is a random variable with the following distribution. $$ \begin{array}{lllll} \text { Demand } & 0 & 1 & 2 & 3 \\ \mathrm{P}(\mathrm{D}) & 1 / 9 & 6 / 9 & 1 / 9 & 1 / 9 \end{array} $$ When the inventory level reaches 3, production is stopped until the inventory drops to \(2 .\) Let the states of the system be the inventory level. The transition matrix is found to be Assuming the industry starts with zero inventory find the transition matrix as \(\mathrm{n} \rightarrow \infty\).

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks