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

Answer:

There were 15 lions and 19 hyenas.

Step-by-step 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.