Count complete promotion bundles
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. marks
[2021/NJC/Promo/2]
Solution
Bundles and discounts
A candy shop's Halloween sale: 20% off every chocolate bar, a $2 discount for every 3 bags of gummy bears, and every 6 lollipops for the price of 5. Jo bought 5 chocolate bars, 3 bags of gummy bears and 36 lollipops for $65.20. Hannah bought 4, 14 and 24 for $119.84. Pete bought 17, 5 and 20 for $89.12. Calculate the original selling price of each of a chocolate bar, a bag of gummy bears and a lollipop.
Hint
Let be the original prices.
For each person, work out the discount in terms of complete bundles: how many groups of 3 bags? how many groups of 6 lollipops?
Write each bill as one equation.
The $2 discount applies only to each *complete* group of 3 bags; left-over bags pay full price.
Every complete group of 6 costs , so is valid for 36 lollipops. For 20, apply the deal to 18 only, then pay full price for the remaining 2: .
Answer · Q
Chocolate bar 2.70 dollars, gummy-bear bag 6.80 dollars, lollipop 1.20 dollars.
Jo: 5 bars, 3 bags, 36 lollipops
5 bars at 80%; 3 bags is one complete bundle (); 36 lollipops is 6 complete bundles of 6, each costing .
Hannah: 4 bars, 14 bags, 24 lollipops
14 bags = 4 bundles of 3 plus 2 left over, so 4 discounts of $2: . 24 lollipops are 4 bundles of 6.
Pete: 17 bars, 5 bags, 20 lollipops
5 bags = 1 bundle + 2 left over: one $2 discount. 20 lollipops = 3 bundles of 6 (cost each) plus 2 left over at each: .
Solve
By calculator. Check Jo: ✓.
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