# 40 species of animals live in the forest: 7 species more carnivores than ungulates, and 2 species more rodents that carnivores. How many ungulates live in the forest?

May 30, 2017

Number of ungulates is 8.

#### Explanation:

C is for carnivores, U is for ungulates, and R is for rodents.

For carnivores: $C = 7 + U$ can be written
For rodents: $R = 2 + C$ can be written.
For rodents, instead of C, you can write the first equation (7+U) yielding
For rodents: $R = 2 + 7 + U$

Now you have 3 components for your equation, each component contains U term.

$40 = \left(7 + U\right) + U + \left(2 + 7 + U\right)$

$40 = 16 + 3 U$

$40 - 16 = 3 U$

$24 = 3 U$

$8 = U$

Number of ungulates is 8.