Question: Topic 1: Applications of linear equations and their graphs
Complex familiar
Question 4 (4 marks)
A family has a small farm with chickens and cows. The total number of chickens and cows is $23$ and, combined, they have $56$ legs. Calculate how many cows and chickens there are on the farm.
a=$2$ b=$4$ =$23$ ab=$23=56$
1. **State the problem:**
We have a farm with chickens and cows. The total number of animals is $23$, and the total number of legs is $56$. We want to find how many chickens and cows there are.
2. **Define variables:**
Let $x$ = number of chickens
Let $y$ = number of cows
3. **Write equations based on the problem:**
- Total animals: $$x + y = 23$$
- Total legs: Chickens have 2 legs each, cows have 4 legs each, so:
$$2x + 4y = 56$$
4. **Solve the system of equations:**
From the first equation:
$$x = 23 - y$$
Substitute into the second equation:
$$2(23 - y) + 4y = 56$$
Simplify:
$$46 - 2y + 4y = 56$$
$$46 + 2y = 56$$
Subtract 46 from both sides:
$$2y = 56 - 46$$
$$2y = 10$$
Divide both sides by 2:
$$\cancel{2}y = \cancel{2}5$$
$$y = 5$$
5. **Find $x$:**
$$x = 23 - y = 23 - 5 = 18$$
6. **Answer:**
There are $18$ chickens and $5$ cows on the farm.