PSLE
In a shop, candles are sold only in boxes. A box of 9 short candles costs $2.70 and a box of 6 long candles costs $5.00.

1. Valen wants 16 short candles and 3 long candles for his lanterns. What is the least amount of money that Valen will need to spend on the candles?
2. Natalie bought 21 more long candles than short candles from the shop. The total number of candles she bought was fewer than 80. How much did Natalie spend on the candles altogether?

(a)
Number of sets of 9 short candles
= 16 ÷ 9
= 1 r 7

Number of boxes of short candles that Valen needs to buy
= 1 + 1
= 2

Amount that Valen needs to spend on short candles
= 2 x 2.70
= $5.40

Least amount that Valen will need to spend
= 5.40 + 5.00
= $10.40

(b)

Packets of long candles	Number of long candles  (x6)	Packets of short candles	Number of short candles (x9)	Total	Difference	Check
10	60	2	18	78	60 - 18 = 42	x
9	54	2	18	72	54 - 18 = 36	x
8	48	3	27	75	48 - 27 = 21	✓

To know the number of packets of long candles and short candles, we list the multiplies of 6 and 9.
We use systematic listing to find the difference between the number of long candles and short candles so that we can find the right combination that will result in having 21 more long candles.
We also check if the total number of candles must be less than 80.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78 
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72 

Number of packets of long candles = 8

Cost of long candles
= 8 x 5.00
= $40.00

Cost of short candles
= 3 x 2.70
= $8.10

Total amount that Natalie spent on the candles
= 40.00 + 8.10
= $48.10

Answer(s): (a) $10.40; (b) $48.10