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There are 40 cows and chickens in the farmyard. One quiet afternoon, Jack counted and found that there were 100 legs in all. How many cows and how many chickens are there?

Solve this problem by writing and solving an equation.

Guest Aug 25, 2017

#1
+351
+1

Well, you know that cows have four legs and chickens have 2 legs. (Unless they somehow got mutated...)

Let's used the variable 'x' for the number of cows and 'y' for the number of chickens.

I think there would be 2 equations here.

There are 40 cows and chickens, so 1 equation would be:

x+y=40

Here is the second equation.

Cows have 4 legs. Chickens have 2 legs. There are 100 legs in all.

So... you would have to make another equation.

4x + 2y = 100.

To solve, you would need to use both of these equations.

I used the substitution method because it is easier to explain by typing...  :)

Look at the first equation. x+y=40.

Subtract y to both sides and get x=40-y.

Now, look at the second equation. 4x + 2y = 100.

We can substitute x for 40 -y because x=40-y. We figured that out from the first equation.

Let's calculate

4(40-y) + 2y =100.

Distribute:

160-4y+2y=100

Simplify:

160-2y=100

Subtract 160 to both sides:

-2y=-60

Divide both sides by -2:

y=30

So we finally got y. Let's try to find x. Remember that x=40-y. Substitute 30 for y:

x=40-30

x=10

Cows were x and chickens were y.

There were 10 cows and 30 chickens in total.

That's a lot of meat...

Gh0sty15  Aug 25, 2017
Sort:

#1
+351
+1

Well, you know that cows have four legs and chickens have 2 legs. (Unless they somehow got mutated...)

Let's used the variable 'x' for the number of cows and 'y' for the number of chickens.

I think there would be 2 equations here.

There are 40 cows and chickens, so 1 equation would be:

x+y=40

Here is the second equation.

Cows have 4 legs. Chickens have 2 legs. There are 100 legs in all.

So... you would have to make another equation.

4x + 2y = 100.

To solve, you would need to use both of these equations.

I used the substitution method because it is easier to explain by typing...  :)

Look at the first equation. x+y=40.

Subtract y to both sides and get x=40-y.

Now, look at the second equation. 4x + 2y = 100.

We can substitute x for 40 -y because x=40-y. We figured that out from the first equation.

Let's calculate

4(40-y) + 2y =100.

Distribute:

160-4y+2y=100

Simplify:

160-2y=100

Subtract 160 to both sides:

-2y=-60

Divide both sides by -2:

y=30

So we finally got y. Let's try to find x. Remember that x=40-y. Substitute 30 for y:

x=40-30

x=10

Cows were x and chickens were y.

There were 10 cows and 30 chickens in total.

That's a lot of meat...

Gh0sty15  Aug 25, 2017
#2
+76069
0

Good job , Gh0sty....!!!

CPhill  Aug 25, 2017

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