a pet shop has a total of 17 dogs and birds. Altogether there are 48 feet. How many dogs are ther and how many birds?
6.8
2b+4d=48 assuming dogs have four feet, birds two.
b+d=17
b=17-d
2(17-d)+4d=48
34+2d=48
d=7
b=10
Let's assign variables to represent the number of dogs and birds. Let D represent the number of dogs, and B represent the number of birds.
We know that the total number of dogs and birds is 17:
D + B = 17 ---(1)
We also know that the total number of feet is 48. Since dogs have 4 feet and birds have 2 feet, we can set up the equation:
4D + 2B = 48 ---(2)
To solve these equations, we can use the substitution method.
1. Solve equation (1) for D:
D = 17 - B
2. Substitute this value of D into equation (2):
4(17 - B) + 2B = 48
3. Simplify and solve for B:
68 - 4B + 2B = 48
-2B = 48 - 68
-2B = -20
B = -20 / -2
B = 10
4. Substitute the value of B back into equation (1) to find D:
D + 10 = 17
D = 17 - 10
D = 7
Therefore, there are 7 dogs and 10 birds in the pet shop.
To determine the number of dogs and birds, we can set up a system of equations based on the given information.
Let's assume the number of dogs is represented by 'x,' and the number of birds is represented by 'y.'
1. The total number of dogs and birds is 17: x + y = 17.
2. The total number of feet can be calculated by multiplying the number of dogs by 4 (since each dog has 4 feet) and the number of birds by 2 (since each bird has 2 feet). Thus, 4x + 2y = 48.
Now that we have two equations, we can use different methods to solve them simultaneously. One possible method is substitution.
1. Solve the first equation for either x or y. Let's solve it for x:
x = 17 - y.
2. Substitute this value of x into the second equation:
4(17 - y) + 2y = 48.
3. Simplify and solve for y:
68 - 4y + 2y = 48,
-2y = 48 - 68,
-2y = -20,
y = (-20)/(-2),
y = 10.
Now that we know there are 10 birds, we can substitute this value back into the first equation to find the number of dogs:
x + y = 17,
x + 10 = 17,
x = 17 - 10,
x = 7.
Therefore, there are 7 dogs and 10 birds in the pet shop.