[SPM Add Math Johor 2021 P1 Q15] How to solve this question?

Fifi, seorang ahli kimia mempunyai tiga jenis larutan. Larutan yang pertama mengandungi 10 % asid, larutan kedua mengandungi 40% asid manakala larutan yang ketiga pula mengandungi 60% asid.

Pada suatu hari, Fifi ingin membuat larutan yang menggunkan tiga jenis larutan. Fifi ingin menyediakan 500 liter campuran larutan yang mengandungi 45% asid. Bekalan larutan yang mengandungi 10% asid adalah dua kali bekalan yang mengandungi 40% asid. Bolehkah anda mencadangkan berapakah isipadu setiap larutan yang perlu digunakan oleh Fifi?

Fifi, a chemist, has three types of solutions. The first solution contain 10% of acid, the second solution 40% of acid and the third solution 60% of acid.

One day, Fifi intends to prepare a solution from three types of solutions. Fifi intends to prepare 500 litres of mixed solution with an acid concentration of 45%. The available amount of 10% acid solution is twice the amount of 40% acid solution. How much of each solution would you suggest Fifi use? [8 marks]


Hi Farhaini,
The first step would be to identify what chapter this question belongs to. The question asks how much of each solution, so from there we can conclude it’s a question with multiple unknowns, thus this has something to do with simultaneous equations.

The next helpful step is to simplify the given information into a table form (or however you like that makes it easy to you)

We know that the 3 volumes used must add up to 500L. I think that the question should’ve phrased it in a better way to avoid confusion: the volume of the 10% acid used (let’s call it x) is twice of that of the volume of 40% acid used. (Let’s call it y)

Since we know that x=2y, we can directly substitute it so that it is an equation with 2 unknowns.

The other equation is a bit hard to explain- since I took the old SPM syllabus, I could only think of an explanation in terms of chemistry, maybe under the new syllabus there is another explanation for it though :joy:

It’s like adding a moles from solution 1, b moles from solution 2, and c moles from solution 3, and the total number of moles in the solution is a+b+c.

From chemistry we know that
[ moles=MV= molarity × volume ]
I would convert the 10%, 40%, and 60% into a decimal form: 0.10, 0.40 and 0.60 respectively.

So the second equation would be in the form of:
M_1V_1 + M_2V_2 + M_3V_3=M_{total}V_{total}

We need not worry about the units here as it’s the same on both LHS and RHS.

And the last step is quite standard:

So the final answer:
Fifi should use 125L of 10% acid solution,
62.5L of 40% acid solution and
312.5L of 60% acid solution.

Personally find this question kind of poorly phrased and unfair haha :joy:

Hope this helps! :slight_smile:

1 Like

Very interesting explanation ! First time I knew that we can solve Addmaths questions by using the knowledge of Chemistry :relaxed: Thank you very much! :hugs::blush::grinning_face_with_smiling_eyes:

1 Like