Question

In a zoo, three lions and four tigers eat 390 kg of food every week. In another zoo, four lions and five tigers eat 500 kg of food every week. Lions and tigers eat different amounts of food, but all individuals of the same species eat the same amount. The amount of food a single lion eats per week is _______ kg. (Answer in integer)

Answer 1

Correct Answer: 50

Step 1: Translate word problem into equations.
\[ \begin{aligned} 3L + 4T &= 390 \quad\text{(Zoo 1)} \tag{1}
4L + 5T &= 500 \quad\text{(Zoo 2)} \tag{2} \end{aligned} \]

Step 2: Eliminate one variable (classic \(2\times 2\) system).
Multiply (1) by \(4\) and (2) by \(3\) to align \(L\):
\(\;\) \(12L + 16T = 1560\) \quad (1')
\(\;\) \(12L + 15T = 1500\) \quad (2')
Subtract (2') from (1'): \((12L-12L) + (16T-15T) = 1560-1500 \Rightarrow T=60\).

Step 3: Back-substitute to get \(L\).
From (1): \(3L + 4(60) = 390 \Rightarrow 3L + 240 = 390 \Rightarrow 3L=150 \Rightarrow L=\boxed{50}\).

Step 4: Consistency check in the second equation.
\(4L + 5T = 4(50) + 5(60) = 200 + 300 = 500\) — matches the given amount.