Question

A certain zoo has mammal and reptiles and birds, and no other animals. The ratio of mammals to reptiles to birds is 11: 8:5. How many birds are in the zoo?

Answer 1

Given this ratio, we could say that there are:

11x mammals

8x reptiles

5x birds

for some value of x.

Statement 1: there are twelve more mammals in the zoo than there are reptiles

We can write: number of mammals = number of reptiles + 12

Or we can write: 11x = 8x + 12

Solve to get x = 4

Once we know the value of x, we can see that the number of birds = 5x = (5)(4) = 20

Statement 2: if the zoo acquired 16 more mammals, the ratio of mammals to birds would be 3:1

So, (current number of mammals + 16)/(current number birds) = 3/1

Or we can write: (11x +16)/5x = 3/1

Cross multiply to get: 11x + 16 = 15x

Solve, to get x = 4

Once we know the value of x, we can see that the number of birds = 5x = (5)(4) = 20