At the park the other day I saw 22 ducks and dogs.I counted 60 legs.How many of the animals were ducks and how many were dogs?
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To solve this problem, we need to set up a system of equations based on the information given. Let's represent the number of ducks as 'D' and the number of dogs as 'G'.
We know that each duck has 2 legs and each dog has 4 legs. So, the total number of legs can be expressed as follows:
2D (the number of duck legs) + 4G (the number of dog legs) = 60.
We also know that the total number of animals (ducks + dogs) is 22, so:
D + G = 22.
We now have a system of equations:
2D + 4G = 60,
D + G = 22.
To solve this system, we can use the substitution or elimination method. Let's use substitution:
From the second equation, we can express D as 22 - G.
Substitute this expression for D in the first equation:
2(22 - G) + 4G = 60.
Now, simplify and solve for G:
44 - 2G + 4G = 60,
2G = 16,
G = 8.
So, there are 8 dogs (G) at the park. We can plug this value into the second equation to find the number of ducks (D):
D + 8 = 22,
D = 22 - 8,
D = 14.
Therefore, there are 14 ducks and 8 dogs at the park.