Question

Solve using linear systems

At a dog show in Calgary, between the number of humans and the number of dogs, there were a total of 36 heads and 102 legs in the ring. How many dogs were in the ring?

Answer 1

15 dogs

Explanation:

Both dogs and humans have 1 head each

A dog has 4 legs and a human has 2

Assume there were x dogs and y humans

Let's write 2 equations according to the given information and put them into a system:

{x + y = 36,

{4x + 2y = 102;

Make x the subject from the 1st equation:

x = 36 - y

Replace x in the 2nd equation with its value from the 1st one:

4(36 - y) + 2y = 102

144 - 4y + 2y = 102

Collect like-terms:

-2y = -42 / : (-2)

y = 21

x = 36 - 21 = 15

Since we've marked x as the number of dogs, we've got the answer (15 dogs)