A local animal shelter had four more than six times as many adult cats as kittens. After eight of the kittens were adopted, the shelter had four fewer than eight times as many adult cats as kittens. How many adult cats are at the shelter?
kittens --- x
adult cats -- 6x+4
after adoption:
kittens = x-8
6x+4 = 8(x-8) - 4
6x + 4 = 8x - 64 - 4
-2x = -72
x = 36
Number of adults has not changed, so there are
6(36) + 4 or 220 adult cats
check:
originally..
number of kittens 36
cats = 220
is 6(36) + 4 = 220 ? yes
after adoption:
kittens = 28
is 8(28)-4 = 220 ? YES
My answer is correct
At the local animal shelter, there are 30 cats and 36 dogs. What is the ratio of dogs to cats at the local animal shelter
To solve this problem, we will set up equations based on the given information and solve them simultaneously.
Let's denote the number of kittens as "K" and the number of adult cats as "A."
According to the first statement, the number of adult cats is four more than six times the number of kittens. We write this as:
A = 6K + 4 -- Equation 1
According to the second statement, after eight kittens were adopted, the shelter had four fewer than eight times as many adult cats as kittens. We write this as:
A - 8 = 8K - 4 -- Equation 2
Now we will solve these equations together:
From Equation 1, we can rewrite it as:
A - 6K = 4 -- Equation 3
Substituting Equation 3 into Equation 2:
(6K + 4) - 8 = 8K - 4
Simplifying the equation:
6K - 4 = 8K - 12
Rearranging the equation:
8K - 6K = 12 - 4
2K = 8
K = 4
Now, substitute the value of K back into Equation 1 to find the number of adult cats:
A = 6(4) + 4
A = 24 + 4
A = 28
Therefore, there are 28 adult cats at the shelter.