Systems of Equations Help
I have a systems of equations word problem that I need help with:
Since my uncles farmyard appears to be overrun with dogs, and chickens, I asked him how many of each he had. He responded that his dogs and chickens had a total of 148 legs and 60 heads. How many dogs and how many chickens does my uncle have?
Karin From Algebra Class Says:
This is a very interesting problem!
This is a problem that can be solved using a system of equations.
In order to write a system of equations, you must have two variables, so ask yourself, what two things do I need to know?
You need to know how many dogs and how many chickens. So, we're going to let x= the number of dogs and y = the number of chickens.
Now we need to write two equations. We know information about two things: the number of legs and the number of heads.
Let's write an equation about the number of legs. How many legs does a dog have? 4. How many legs does a chicken have? 1.
4x + 2y = 148 (4 legs times number of dogs & 2 legs times number of chickens)
Now lets write an equation about the number of heads. How many heads does a dog have? 1. How many heads does a chicken have? 1.
x + y = 60. (Since each only has one head, we do not need to write the coefficient, 1).
Now you need to solve your the system of equations:
4x + 2y = 148
x + y = 60.
I would use the substitution method.
x + y = 60 can be rewritten as y = -x + 60
Substitute this into the first equation for y.
4x + 2(-x + 60) = 148
4x -2x + 120 = 148
2x + 120 = 148
2x +120 -120 = 148 - 120
2x = 28
2x/2 = 28/2
x = 14
Then substitute your value for x into the second equation and solve.
14 + y = 60
14 -14 + y = 60 - 14
y = 46
There were 14 dogs and 46 chickens.
Hope this helps.
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