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Farmer looks over a field and she’s 35 heads and 106 feet. Summer pigs, summer ducks. How many of each animal are there?

User Tharaka
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1 Answer

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23 votes

EXPLANATION

If the field is 35 heads and 106 feet

Let x be the number of pigs and y the number of ducks.

x= number of pigs y= number of ducks

Each pig has one head and 4 feet and each duck has 1 head and 2 feets.

The first equation about the heads would be as follows:

(1) x + y = 35

The second equation about the legs would be:

(2) 4x + 2y = 106

Isolating x in (1):

x = 35 - y

Replacing x= 35 - y in (2):

4(35-y) + 2y = 106

Applying the distributive property:

140 - 4y + 2y = 106

Adding like terms:

140 -2y = 106

Adding +2y to both sides:

140 = 106 + 2y

Subtracting -106 to both sides:

140 - 106 = 2y

Subtracting numbers:

34 = 2y

Dividing both sides by 2:

34/2 = y

Simplifying:

17 = y

Switching sides:

y = 17

Replacing y=17 in (1)

x + 17 = 35

Subtracting -17 to both sides:

x = 35 - 17

Subtracting numbers:

x = 18

The solutions to the system of equations are:

x= 18 and y = 17

Hence, there are 18 pigs and 17 ducks in the farm.

User Thisisashwani
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