Question

At an animal shelter, the ratio of cats to dogs is 5 : 3. If there are 104 animals at the shelter, how many cats are there?

Answer 1

Step-by-step explanation:

Let number of cats be x

and number of dogs be y

Then as given, ratio of cats to dogs is 5:3,

let k be a same value to be multiplied get total animals,

x + y = 104

that is 5k +3k = 104

8k =104

k = 104/8

k = 13

so number of cats= 5k = 5 x 13 = 65

number of dogs = 3k = 3 x 13 = 39

Answer 2

Given :

• At an animal shelter, the ratio of cats to dogs is 5:3.
• There are 104 animals at the shelter.

To find :

• How many cats are there ?

Solution :

Let the number of cats be x and the number of dogs be y.

According to 1st condition :-

• The ratio of cats to dogs is 5:3 .

$\implies\sf{x:y=5:3}$

$\implies\sf{\frac{x}{y}=\frac{5}{3}}$

$\implies\sf{5y=3x}$

$\implies\sf{y=\frac{3x}{5}......eq(1)}$

According to 2nd condition :-

• There are 104 animals at the shelter.

$\implies\sf{x+y=104}$

✪ Put y=$\frac{3x}{5}$ from eq (1) ✪

$\implies\sf{x+\frac{3x}{5}=104}$

$\implies\sf{\frac{8x}{5}=104}$

$\implies\sf{8x=104\times\:5}$

$\implies\sf{x=\frac{104\times\:5}{8}}$

$\implies\sf{x=65}$

Therefore, there are 65 cats at the animal shelter.