PSLE
In a shop, candles are sold only in boxes. A box of 7 short candles costs $3.10 and a box of 5 long candles costs $4.60.

1. Dylan wants 16 short candles and 4 long candles for his lanterns. What is the least amount of money that Dylan will need to spend on the candles?
2. Joelle bought 19 more long candles than short candles from the shop. The total number of candles she bought was fewer than 70. How much did Joelle spend on the candles altogether?

(a)
Number of sets of 7 short candles
= 16 ÷ 7
= 2 r 2

Number of boxes of short candles that Dylan needs to buy
= 2 + 1
= 3

Amount that Dylan needs to spend on short candles
= 3 x 3.10
= $9.30

Least amount that Dylan will need to spend
= 9.30 + 4.60
= $13.90

(b)

Packets of long candles	Number of long candles  (x5)	Packets of short candles	Number of short candles (x7)	Total	Difference	Check
10	50	2	14	64	50 - 14 = 36	x
9	45	2	14	59	45 - 14 = 31	x
8	40	3	21	61	40 - 21 = 19	✓

To know the number of packets of long candles and short candles, we list the multiplies of 5 and 7.
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 19 more long candles.
We also check if the total number of candles must be less than 70.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 

Number of packets of long candles = 8

Cost of long candles
= 8 x 4.60
= $36.80

Cost of short candles
= 3 x 3.10
= $9.30

Total amount that Joelle spent on the candles
= 36.80 + 9.30
= $46.10

Answer(s): (a) $13.90; (b) $46.10