Do You Love to see the circus?

Algebra Level pending

A circus party has same number of $Lions$ as $Tigers.$ You asked to the owner of the circus the number of $lions$ and $tigers.$ The owner was a very funny person and he gave you the following information :

$(i)$ $An$ $elephant$ is enough to feed all the $tigers$ and $lions$ in the circus.

$(ii)$ $18$ deer produce the same amount of meat as $an$ $elephant$ does.

$(iii)$ A $Lion$ eats $twice$ as a $Tiger$ .

$(iv)$ $1$ $buffalo$ is enough to feed a $Lion$ and a $Tiger$ .

$(v)$ A $Tiger$ will eat exactly the same amount of meat a $deer$ has.

Find the number of $Tigers$ and $Lions$ in that circus party.

The answer is 6.

2 solutions

Abdullah Ahmed
Jun 28, 2016

Let the number of tigers (and lions) be $x$

$1$ All of $2x$ animals eat in total $3x$ (a single tiger's food)

$2$ $3x$ (a single tiger's food) = an elephant.

$3$ $3x$ (a single tiger's food) = $18$ deer .

$4$ $3x$ (a single tiger's food) = 18(a single tiger's food)

So, $3x$ = $18$

$x$ = $6$ .

Hung Woei Neoh
Jul 1, 2016

Let number of lions = number of tigers = $x$

Let the amount a lion eats be $a$ and the amount a tiger eats be $b$

Let the amount of meat an elephant has be $e$ , and the amount of meat a deer has be $d$

From the information given:

$e=ax+bx$
$e=18d$
$a=2b$
Irrelevant information
$b=d$

Substitute (2) into (1):

$18d=ax+bx\implies$ (6)

Next, substitute (3) into (6):

$18d=(2b)x+bx \implies 18d=3bx\implies$ (7)

After that, substitute (5) into (7):

$18d=3dx \implies x=\dfrac{18d}{3d} = \boxed{6}$

Do You Love to see the circus?

The answer is 6.

2 solutions

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