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Chapter 0: Problem 58

Write an original word problem that can be solved using a linear equation. Then solve the problem.

Short Answer

Expert verified
The farmer has 15 chickens and 7 cows.

Step by step solution

01

Formulate the word problem

Imagine a farmer who has chickens and cows in his farm. In total, he has 22 animals and 58 legs. Since a chicken has 2 legs and a cow has 4 legs, how many chickens and cows does the farmer have? We can solve this problem by using the method of solving linear equations.
02

Represent the problem using equations

Let's denote the number of chickens as \( x \) and the number of cows as \( y \). We know that the total number of animals is 22, so we can write the first equation as \( x + y = 22 \). Moreover, we know that the total number of legs is 58. Since each chicken has 2 legs and each cow has 4, we can write the second equation as \( 2x + 4y = 58 \).
03

Solve the system of equations

Now we have a system of two linear equations. To solve them, we can first simplify the second equation by dividing it by 2. This gives us \( x + 2y = 29 \). Subtracting the first equation from the new second equation gives \( y = 7 \). Substituting \( y = 7 \) into the first equation gives \( x = 15 \). Therefore, the farmer has 15 chickens and 7 cows.

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