a farmer has both cickens and cattle.These animals have a total of 40 heads and 140 feet.How many chicken and how many cattle has this farmer
number of chickens --- x
number of cattle ---- y
x+y = 40
2x + 4y = 140 or x+2y = 70
subtract them
y = 30
then x = 10
The farmer has 10 chickens and 30 cattle
check:
10+30 = 40 heads
20 chicken feet + 120 cattle feet = 140 feet
To solve this problem, we can use a system of equations. Let's assume that the number of chickens is represented by 'c', and the number of cattle is represented by 't'.
From the given information, we know that:
1. Each animal has one head, so the total number of heads is represented by the equation: c + t = 40.
2. Chickens have two feet and cattle have four feet, so the total number of feet is represented by the equation: 2c + 4t = 140.
Now, we can solve this system of equations to find the values of 'c' and 't'.
First, let's rewrite the first equation to solve for 'c':
c = 40 - t.
Substituting this value of 'c' into the second equation, we get:
2(40 - t) + 4t = 140.
Simplifying the equation:
80 - 2t + 4t = 140.
2t = 140 - 80.
2t = 60.
t = 60 / 2.
t = 30.
Now, substitute the value of 't' back into the first equation to find 'c':
c + 30 = 40.
c = 40 - 30.
c = 10.
Therefore, the farmer has 10 chickens and 30 cattle.