Note: Method by Khong is basically algebra and can be used in most of the P6/S1 questions for solution. Not sure about others, but feedback from my child is that P6 Math teacher discourages use of algebra because it usually presents “one-liner” workings with very little method marks that can be awarded if answer turns out to be wrong. Of course, full marks will be awarded for correct ending answer. Although the decision depends on the proficiency of individual students applying algebraic equations, there are definitely instances where the more advanced students are penalised completely for carelessness in a “one-liner” equation forming. So the discouragement.
Maybe that is why algebra for solving problem sums was not the intention of PSLE syllabus. Although I must admit the many Heuristics methods (units and parts) are like the basics of algebra and the lines between the two start to blur. As kids/parents/teachers/tutors get more used to and become proficient with “u”, and begin to apply “u” like the “x” we are used to in algebra, that is when it has unwittingly evolved from P6 Heuristics to solving by algebraic equations.
So much for my long-windedness… I feel the intention of the question was that each bundle is not separable (should mention), so rather than divide the cost to each piece, the purpose is to know LCM is 12 for bundle of 4 and bundle of 3, and to understand the concept that there is minimum of 12 pcs for equal quantity sets and work on from there. (like Ace Starling)
[just for interest: Suppose the difference is $15.30 instead $37.40. That is when the “bundle” is broken up (not likely intention of setter in PSLE) and best solved with the above solution by Khong. See below.]
Method A (continuing from Ace Starling)
$15.30/$3.40 = 4.5 (times of 12 pcs set)
54 pcs each (there are 13.5 sets of pen bundle of 4)
Method B (continuing from Khong)
0.95u = 2u / 3 +
2.85u = 2u +45.90
u=54 pcs each (there are 13.5 sets of pen bundle of 4)