Answer:
Number of dogs = 30
Number of cats = 20
Explanation:
We can determine how many dogs and cats the pet store has using a system of equations, where:
- d represents the number of dogs,
- and c represents the number of cats.
First equation: Since we're told that the sum of the numbers of dogs and cats is 50, our first equation is given by:
d + c = 50
Second equation: Since we're told that the difference of the numbers of dogs and cats is 10 (and that there are more dogs than cats), our second equation is given by:
d - c = 10
Method to solve: Substitution:
Solving for d:
The two equations are already arranged in a way that allows us to eliminate c (c - c = 0) and solve for d, when we add the two equations:
d + c = 50
+
d - c = 10
----------------------------------------------------------------------------------------------------------
(d + d) + (c - c) = (50 + 10)
(2d = 60) / 2
d = 30
Thus, the pet store has 30 dogs.
Solving for c:
Now we can solve for c by plugging in d for 30 in the first equation in our system:
(30 + c = 50) - 30
c = 20
Thus, the pet store has 20 cats.