A pet shop has a total of 17 dogs and birds. Altogether there are 48 feet. How many dogs are there and how many birds?
dogs ---> x
birds --> 17-x
4(x) + 2(17-x) = 48
solve for x
Let's assume the number of dogs as 'x' and the number of birds as 'y'.
Each dog has 4 legs and each bird has 2 legs.
So, the total number of legs can be expressed as:
4x (for dogs) + 2y (for birds) = 48
Given that there are a total of 17 dogs and birds:
x + y = 17
Now we have a system of equations:
4x + 2y = 48
x + y = 17
We can solve this system of equations to find the values of x and y.
To find the number of dogs and birds in the pet shop, we need to set up a system of equations based on the given information.
Let's say the number of dogs is represented by 'd', and the number of birds is represented by 'b'.
Since each dog has 4 feet and each bird has 2 feet, we can determine the total number of feet using the formula:
Total Number of Feet = (Number of Dogs * 4) + (Number of Birds * 2)
Given that there are 17 dogs and birds in total, we can write the equation:
d + b = 17 (Equation 1)
Given that there are 48 feet in total, we can write the equation:
(4 * d) + (2 * b) = 48 (Equation 2)
Now we have a system of two equations with two unknowns. We can solve these equations simultaneously to find the values of 'd' and 'b'.
To solve the system of equations, there are various methods such as substitution, elimination, or matrix method. Let's use the substitution method.
From Equation 1, we can express 'd' in terms of 'b':
d = 17 - b
Substituting this expression for 'd' into Equation 2, we get:
(4 * (17 - b)) + (2 * b) = 48
Simplifying the equation:
68 - 4b + 2b = 48
68 - 2b = 48
Subtracting 68 from both sides of the equation:
-2b = -20
Dividing both sides of the equation by -2:
b = 10
Now that we have the value of 'b', we can substitute it back into Equation 1 to find the value of 'd':
d + 10 = 17
Subtracting 10 from both sides of the equation:
d = 7
Therefore, there are 7 dogs and 10 birds in the pet shop.