the trainers took a count of the animals at the zoo. there are both birds and four legged mammals at the zoo. the trainers counted 550 feet and 155 animals on their first trip through. How many birds and mammals are there?
15
x=number of 2 legged birds
y=number of 4 legged mammals
2x+4y=550
if there are a total of 155 animals and you know the number of 2 legged birds, you could subtract the two and find the number of 4 legged mammals
therefore, let y=155-x
substitution:
2x+4(155-x)=550
solve for x. that is the number of 2 legged birds!
then plug x into y=155-x and that will be the number of four legged mammals
Let's assign variables to represent the number of birds and four-legged mammals. Let's say the number of birds is represented by 'b', and the number of mammals is represented by 'm'.
We know that birds have 2 feet, and mammals have 4 feet.
To get the total number of bird feet, we multiply the number of birds by 2. So, the total number of bird feet is 2b.
To get the total number of mammal feet, we multiply the number of mammals by 4. So, the total number of mammal feet is 4m.
The sum of the bird feet and mammal feet should be equal to the total number of feet counted by the trainers, which is 550. We can write this as an equation:
2b + 4m = 550
We also know that the total number of animals is 155. So we can write another equation:
b + m = 155
Now we have a system of equations:
2b + 4m = 550
b + m = 155
To solve the system of equations, we can use substitution or elimination methods. For this example, let's use the substitution method:
Let's solve the second equation for m:
m = 155 - b
Now we substitute this value for m in the first equation:
2b + 4(155 - b) = 550
Simplifying the equation:
2b + 620 - 4b = 550
Combine like terms:
-2b + 620 = 550
Subtract 620 from both sides:
-2b = -70
Divide both sides by -2:
b = 35
We have found the value of 'b', which represents the number of birds.
Now substitute this value back into the second equation to find 'm':
35 + m = 155
m = 155 - 35
m = 120
So, there are 35 birds and 120 mammals at the zoo.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the number of birds is 'b' and the number of four-legged mammals is 'm'.
We know that each bird has 2 feet, and each mammal has 4 feet. So, the total number of feet can be represented as:
2b + 4m = 550 (Equation 1)
We also know that the total number of animals is given as:
b + m = 155 (Equation 2)
Now, we can solve this system of equations to find the values of 'b' and 'm'.
To eliminate the 'b' variable, let's multiply Equation 2 by 2:
2(b + m) = 2(155)
2b + 2m = 310 (Equation 3)
Now, let's subtract Equation 3 from Equation 1:
2b + 4m - (2b + 2m) = 550 - 310
2b + 4m - 2b - 2m = 240
2m = 240
m = 240/2
m = 120
Now, substitute the value of 'm' into Equation 2 to find the value of 'b':
b + 120 = 155
b = 155 - 120
b = 35
So, there are 35 birds and 120 mammals at the zoo.