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

[Far]

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]

[D.B]

Answer

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

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

Hope this helps!

[Far]

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