A nutrient ratio fixes a serving ratio · source reference

Printed question

A Sumo wrestler would like to have fish fillet, salad and fries for breakfast. As he is on a special diet, he must make sure that his intake (in grams) of protein, carbohydrates and fats per meal is in the ratio of 4:8:3. The table below shows the nutritional breakdown for one serving of each item.

Item	Protein (g)	Carbohydrates (g)	Fats (g)
Fish Fillet	150	60	25
Salad with dressing	15	30	5
Fries	5	250	110

Calculate the ratio of the servings of fish fillet, salad and fries that the wrestler should take.

[2009/NJC/Prelim/II/2]

Printed working

Let $x,y,z$ be the number of servings of fish fillet, salad and fries.

$$150x+15y+5z=4k,$$ $$60x+30y+250z=8k,$$ $$25x+5y+110z=3k,$$

where $k$ is a constant.

$$150X+15Y+5Z=4,$$ $$60X+30Y+250Z=8,$$ $$25X+5Y+110Z=3,$$

where $X=\frac{x}{k},Y=\frac{y}{k},Z=\frac{z}{k}$.

Solving simultaneous equations or using GC, $X=0.02,Y=0.06,Z=0.02$. Thus ratio is $1:3:1$.

Teacher notes

Define the variables.

Since ratio of intake is 4:8:3, the actual amounts are $4k,8k,3k$, where $k$ is a constant.

In order to use the GC to solve the simultaneous equations, rewrite the equations in terms of $X,Y,Z$ so that the RHS of the equations are known values.

Printed answer key

$1:3:1$

Source provenance

2025 TJC H2 Math (9758) JC2 MSM: EQUATIONS. Question sheet printed pages 15–19; solution sheet printed pages 1–12. Original exam attribution is retained above. Currency dollar signs are spelled out outside maths to avoid confusing currency with TeX delimiters.