Mie is a volunteer at the animal shelter. The animal shelter has only dogs and cats. 2/5 of the animals are dogs. There are 7 fewer dogs than cats. How many animals are there in the animal shelter?
Answers
Answer:
8
Step-by-step explanation:
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There are 35 animals in the animal shelter.
Given,
(2/5) × total no. of animals = no. of dogs
no. of dogs = no. of cats - 7
To Find,
The no. of animals in the shelter
Solution,
Mie's animal shelter has only dogs and cats.
Let the no. of dogs be x, and the number of cats is y.
Then, the total no. of animals in the shelter will be equal to (x + y)
We have to find the value of x+y
We have been given that (2/5) × total no. of animals = no. of dogs
⇒ (2/5)(x + y) = x
⇒ x + y = (5/2)x
⇒ y = (5/2)x - x
⇒ y = (5-2)/2 x
⇒ y = (3/2) x
Let this be equation (1)
We have also been given that no. of dogs = no. of cats - 7
⇒ x = y - 7
Substitute equation (1) in the above equation:
⇒ x = (3/2)x - 7
⇒ (3/2)x - x = 7
⇒ 1/2 x = 7
⇒ x = 7×2
⇒ x = 14
Substitute this value in equation (1):
⇒ y = (3/2)×14
⇒ y = 3×7
⇒ y = 21
Therefore, the no. of dogs = 14, and the no. of cats = 21
Hence, the total number of animals in the shelter is equal to 35.
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