Question

in a group of dogs and ducks the total number of legs is 170 and the number of heads is 54 find number of dogs in the group?​

Answer 1

Answer:

Number of dogs in the group = 31

Step-by-step explanation:

Let us assume,

Number of dogs = x

Number of ducks = y

Number of legs of

Dogs = 4x

Ducks = 2y

Because dogs have 4 legs and ducks have 2.

So, 4x + 2y = 170

=> 2y = 170 - 4x

=> y = (170-4x)/ 2

Number of heads of

Dogs = x

Ducks = y

Because all have only 1 head.

So, x + y = 54

=> x + (170-4x)/ 2 = 54

=> (2x + 170 - 4x)/2 = 54 {By taking L.C.M}

=> -2x +170 = 108

=> -2x = 108 - 170

=> -2x = -62

=> 2x = 62 {minus and minus will get cancelled on both sides}

=> x = 62/2 = 31

Therefore, number of dogs in the group = 31

Hope this helps you!