Count complete promotion bundles · source reference

Printed question

A candy shop is having a Halloween sale. The items that are on promotion are chocolate bars, gummy bears and lollipops. There is a 20% discount for every chocolate bar purchased, a 2 dollar discount for every 3 bags of gummy bears purchased and every 6 lollipops can be purchased at the price of 5 lollipops.

Hannah, Jo and Pete are preparing for a Halloween party. The table below shows the total bill and the number of chocolate bars, the number of bags of gummy bears and the number of lollipops bought from the candy shop.

Person	Chocolate Bar	Gummy bears	Lollipops	Total Bill (dollars)
Jo	5	3	36	65.2
Hannah	4	14	24	119.84
Pete	17	5	20	89.12

Calculate the original selling price for each of a chocolate bar, a bag of gummy bears and a lollipop. [4]

[2021/NJC/Promo/2]

Printed working

Let $x,y,z$ dollars be the cost of a chocolate bar, a bag of gummy bears and a lollipop respectively.

$5(0.8)x+(3y-2)+30z=65.20$.

$4x+3y+30z=67.20$ — (1).

$4(0.8)x+(14y-8)+20z=119.84$.

$3.2x+14y+20z=127.84$ — (2).

$17(0.8)x+(5y-2)+17z=89.12$.

$13.6x+5y+17z=91.12$ — (3).

From GC, $x=2.70,y=6.80,z=1.20$.

The cost of a chocolate bar, a bag of gummy bears and a lollipop is 2.70, 6.80 and 1.20 dollars respectively.

Teacher notes

Jo: $36=6(6)$. Since every 6 lollipops cost $5z$ dollars (i.e. the price of 5 lollipops), so 36 lollipops cost $6(5z)=30z$ dollars.

Hannah — Gummy Bears: $14=4(3)+2$. Since every 3 bags of gummy bears cost $(3y-2)$ dollars (i.e. 2 dollar discount for every 3 bags purchased), so $12=4(3)$ bags cost $4(3y-2)=(12y-8)$ dollars. The remaining 2 bags cost $2y$ dollars (no discount), so total cost of 14 bags is $(14y-8)$ dollars.

Hannah — Lollipops: $24=4(6)$. 24 lollipops cost $4(5z)=20z$ dollars.

Pete — Gummy Bears: $5=1(3)+2$. Total cost of 5 bags $=[1(3y-2)+2y]=(5y-2)$ dollars.

Pete — Lollipops: $20=3(6)+2$. Remaining 2 cost $2z$ dollars (no discount). Total cost $=[3(5z)+2z]=17z$ dollars.

Printed answer key

The cost of a chocolate bar, a bag of gummy bears and a lollipop is 2.70, 6.80 and 1.20 dollars respectively.

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.