A pet shop has only birds and dogs.If there are 30 pets and they have a total of 86 legs, how many of the pets are birds? please give me the all answer
X birds.
Y dogs.
Eq1: x + y = 30.
Eq2: 2x + 4y = 86.
Multiply Eq1 by -4:
-4x - 4y = -120
+2x + 4y = 86.
Sum: -2x = -34, X = 17 birds.
Let's solve this problem step by step:
Step 1: Assign variables
Let's assign variables to the number of birds and dogs in the pet shop. We'll call the number of birds 'b' and the number of dogs 'd'.
Step 2: Form equations using the information given
From the given information, we have two pieces of information that can be translated into equations:
1. The total number of pets is 30: b + d = 30
2. The total number of legs is 86: 2b + 4d = 86 (as birds have 2 legs and dogs have 4 legs)
Step 3: Solve the equations
We can solve these equations simultaneously to find the values of 'b' and 'd'.
We'll use the method of substitution to solve the equations:
From the first equation, we can express d in terms of b: d = 30 - b
Substituting this value in the second equation, we get:
2b + 4(30 - b) = 86
2b + 120 - 4b = 86
-2b = -34
b = (-34)/(-2)
b = 17
Step 4: Calculate the number of dogs
Using the value of 'b', we can find the number of dogs:
d = 30 - b
d = 30 - 17
d = 13
Step 5: Check the solution
To verify our solution, let's substitute the values of 'b' and 'd' back into the equations:
Equation 1: b + d = 30
17 + 13 = 30 ➜ This equation holds true.
Equation 2: 2b + 4d = 86
2(17) + 4(13) = 86
34 + 52 = 86 ➜ This equation also holds true.
Step 6: Answer the question
The number of birds in the pet shop is 17.
Therefore, there are 17 birds in the pet shop.