Suggested languages for you:

Americas

Europe

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.

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 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.

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

## 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