Question

A zoo keeper weighed some of the animals at Melbourne Zoo. He found that the lion weighs 90 kg more than the leopard, and the tiger weighs 50 kg less than the lion. Altogether the three animals weigh 310 kg. How much does the lion weigh?
(A) 180 kg (B) 150 kg (C) 140 kg (D) 130 kg (E) 100 kg

Answer 1

Li=lion
Le=Leopard
T=tiger

"the lion weighs 90 kg more than the leopard" =>
Li-Le=90, or
Li=Le+90 ............(1)

" tiger weighs 50 kg less than the lion. " =>
Li-T=50, or
T=Li-50, subtitute (1) for Li
T=(Le+90)-50
T=Le+40 .............(2)

"Altogether the three animals weigh 310 kg." =>
Li+Le+T=310 .............(3)

Solve system of 3 equations by substitution:

Substitute (1) in (3)
(Le+90)+Le+T=310

Substitute (2) in (3)
(Le+90)+Le+(Le+40)=310
Isolate and solve for Le
3Le=310-90-40=180
<b>Le=60</b>

Substitute Le in (1)
Li=Le+90=60+90 =>
<b>Li=150</b>

Substitute Le in (2)
T=Le+40=60+40 =>
<b>T=100</b>

Answer 2

150 kg