PSLE In a shop, candles are sold only in boxes. A box of 9 short candles costs $3.80 and a box of 6 long candles costs $5.30.
- Charlie wants 10 short candles and 5 long candles for his lanterns. What is the least amount of money that Charlie will need to spend on the candles?
- Xylia bought 15 more long candles than short candles from the shop. The total number of candles she bought was fewer than 70. How much did Xylia spend on the candles altogether?
(a)
Number of sets of 9 short candles
= 10 ÷ 9
= 1 r 1
Number of boxes of short candles that Charlie needs to buy
= 1 + 1
= 2
Amount that Charlie needs to spend on short candles
= 2 x 3.80
= $7.60
Least amount that Charlie will need to spend
= 7.60 + 5.30
= $12.90
(b)
Packets of long candles
|
Number of long candles (x6) |
Packets of short candles
|
Number of short candles (x9) |
Total
|
Difference
|
Check
|
9 |
54 |
2 |
18 |
72 |
54 - 18 = 36 |
x |
8 |
48 |
2 |
18 |
66 |
48 - 18 = 30 |
x |
7 |
42 |
3 |
27 |
69 |
42 - 27 = 15 |
✓ |
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 15 more long candles.
We also check if the total number of candles must be less than 70.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66
Multiples of 9: 9, 18, 27, 36, 45, 54, 63
Number of packets of long candles = 7
Cost of long candles
= 7 x 5.30
= $37.10
Cost of short candles
= 3 x 3.80
= $11.40
Total amount that Xylia spent on the candles
= 37.10 + 11.40
= $48.50
Answer(s): (a) $12.90; (b) $48.50