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
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
Le=60
Substitute Le in (1)
Li=Le+90=60+90 =>
Li=150
Substitute Le in (2)
T=Le+40=60+40 =>
T=100
150 kg
Let's solve this step by step:
Let's assume the weight of the leopard is x kg.
According to the information given, the lion weighs 90 kg more than the leopard. So, the weight of the lion is x + 90 kg.
And, the tiger weighs 50 kg less than the lion. So, the weight of the tiger is (x + 90) - 50 = x + 40 kg.
Altogether, the three animals weigh 310 kg. So, we can write the equation:
x + (x + 90) + (x + 40) = 310
Simplifying the equation:
3x + 130 = 310
Now, let's isolate the variable term:
3x = 310 - 130
3x = 180
Dividing both sides by 3:
x = 180 / 3
x = 60
So, the weight of the leopard is 60 kg.
Now, we can find the weight of the lion by substituting the value of x back into the equation:
Weight of the lion = x + 90 = 60 + 90 = 150 kg.
Therefore, the lion weighs 150 kg.
So, the answer is (B) 150 kg.
To find out how much the lion weighs, we can start by assigning variables to the weights of the animals. Let's say the weight of the leopard is L kg.
According to the given information, the lion weighs 90 kg more than the leopard, which means the weight of the lion is L + 90 kg.
Similarly, the tiger weighs 50 kg less than the lion. So, the weight of the tiger is (L + 90 kg) - 50 kg.
Now, we can add up the weights of the three animals to get the total weight, which is 310 kg:
L + (L + 90 kg) + [(L + 90 kg) - 50 kg] = 310 kg
Let's simplify the equation:
3L + 130 kg = 310 kg
Now, we can solve for L:
3L = 310 kg - 130 kg
3L = 180 kg
L = 180 kg / 3
L = 60 kg
So, the weight of the lion is L + 90 kg = 60 kg + 90 kg = 150 kg.
Therefore, the lion weighs 150 kg, which corresponds to answer choice (B).