Question

There are a total of 34 lions and hyenas. Each lion eats 4 antelopes a year. Each hyena eats 3 a year. If 117 antelope are eaten in a year, how many lions were there and how many hyenas were there.

Answer 1

There were 15 lions and 19 hyenas.

Explanation:

Given: There are total 34 lions and hyenas. Each lion eats 4 antelopes a year. Each hyena eats 3 a year. Also, 117 antelope are eaten in a year.

To find: Number of lions and hyenas

Let number of lions = x, and

number of hyenas = y

According to question,

`x+y=34` ...(1)

`4x+3y=117` ...(2)

From equation (1),
`y=34-x`.

Substituting
`y=34-x` in equation (2),

`4x+3(34-x)=117`

⇒
`4x+102-3x=117`

⇒
`x+102=117`

⇒
`x=117-102`

⇒
`x=15`

Put
`x=15` in equation
`y=34-x`.

`y=34-15`

⇒
`y=19`

Hence, there were 15 lions and 19 hyenas.