Question

There are a total of 38 animals in a barn. Some are ducks and some are pigs. There are a total of 96 legs in the barn. How many ducks and pigs are there in the barn?

A. 12 ducks and 26 pigs
B. 26 ducks and 12 pigs
C. 14 ducks and 24 pigs
D. 24 ducks and 14 pigs

Answer 1

There are a total of 38 animals in a barn. Some are ducks and some are pigs. There are a total of 96 legs in the barn. C. 14 ducks and 24 pigs are there in the barn

Step-by-step explanation:

Let x be the number of ducks and y be the number of pigs. The total number of animals can be represented as the sum of ducks and pigs:

x + y = 38

The total number of legs can be represented as the sum of the legs of ducks (2 legs each) and pigs (4 legs each):

2x + 4y = 96

Now, we can solve this system of equations to find x and y, representing the number of ducks and pigs, respectively.

From the first equation, we can express x in terms of y:

x = 38 - y

Substitute this into the second equation:

2(38 - y) + 4y = 96

Simplify and solve for y:

76 - 2y + 4y = 96

2y = 20

y = 10

Now that we have y, substitute it back into the expression for x:

x = 38 - 10

x = 28

Therefore, there are 28 ducks and 10 pigs. The correct answer is C. 14 ducks and 24 pigs.

Answer 2

Let's use a system of equations to solve the problem. Let D be the number of ducks and P be the number of pigs.

We have two pieces of information:

1. The total number of animals is 38: D + P = 38

2. The total number of legs is 96 (ducks have 2 legs, pigs have 4 legs): 2D + 4P = 96

Now, let's solve this system of equations.

From the first equation ( D + P = 38 ), we can express D in terms of P: D = 38 - P .

Substitute this expression for D into the second equation:

2(38 - P) + 4P = 96

Simplify and solve for P:

76 - 2P + 4P = 96

Combine like terms:

2P = 20

Divide by 2:

P = 10

Now that we know P = 10, we can find D using the first equation:

D + 10 = 38

Subtract 10 from both sides:

D = 28

So, there are 28 ducks and 10 pigs. Therefore, the correct option is:

**D. 24 ducks and 14 pigs**

Hope this helps :)