Simultaneous linear equations: HCI 2024 Promo Q1

An athlete on a special diet would like to have battered fish fillet, coleslaw and fries for lunch. He must ensure that his intake (in grams) of protein, carbohydrates and fat per meal is $55$g, $130$g, and $70$g respectively. The table below shows the nutritional breakdown for one serving of each item.

Calculate the number of servings of battered fish fillet, coleslaw and fries that the athlete should take for his lunch. [3]

Suggested Solutions

Let $x$, $y$ and $z$ be the number of servings of battered fish fillet, coleslaw and fries respectively. $$\begin{aligned} 20x + 4y + 3z &= 55\\ 20x + 15y + 45z &= 130\\ 15x + 8y + 16z &= 70. \end{aligned}$$ By GC, $x = 2$, $y = 3$, $z = 1$

Therefore, the runner should take $2$ servings of battered fish fillet, $3$ servings of coleslaw and $1$ serving of fries for his lunch.