PSLE In a shop, candles are sold only in boxes. A box of 10 short candles costs $2.80 and a box of 6 long candles costs $5.30.
- Albert wants 30 short candles and 4 long candles for his lanterns. What is the least amount of money that Albert will need to spend on the candles?
- Julie bought 18 more long candles than short candles from the shop. The total number of candles she bought was fewer than 80. How much did Julie spend on the candles altogether?
(a)
Number of boxes of short candles that Albert needs to buy
= 30 ÷ 10
= 3
Amount that Albert needs to spend on short candles
= 3 x 2.80
= $8.40
Least amount that Albert will need to spend
= 8.40 + 5.30
= $13.70
(b)
Packets of long candles
|
Number of long candles (x6) |
Packets of short candles
|
Number of short candles (x10) |
Total
|
Difference
|
Check
|
10 |
60 |
2 |
20 |
80 |
60 - 20 = 40 |
x |
9 |
54 |
2 |
20 |
74 |
54 - 20 = 34 |
x |
8 |
48 |
3 |
30 |
78 |
48 - 30 = 18 |
✓ |
To know the number of packets of long candles and short candles, we list the multiplies of 6 and 10.
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 18 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 10: 10, 20, 30, 40, 50, 60, 70, 80
Number of packets of long candles = 8
Cost of long candles
= 8 x 5.30
= $42.40
Cost of short candles
= 3 x 2.80
= $8.40
Total amount that Julie spent on the candles
= 42.40 + 8.40
= $50.80
Answer(s): (a) $13.70; (b) $50.80