PSLE In a shop, candles are sold only in boxes. A box of 10 short candles costs $3.10 and a box of 7 long candles costs $4.50.
- 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?
- Diana bought 5 more long candles than short candles from the shop. The total number of candles she bought was fewer than 70. How much did Diana spend on the candles altogether?
(a)
Number of sets of 10 short candles
= 16 ÷ 10
= 1 r 6
Number of boxes of short candles that Dylan needs to buy
= 1 + 1
= 2
Amount that Dylan needs to spend on short candles
= 2 x 3.10
= $6.20
Least amount that Dylan will need to spend
= 6.20 + 4.50
= $10.70
(b)
Packets of
long candles
|
Number of
long candles
(x7) |
Packets of
short candles
|
Number of
short candles
(x10) |
Total
|
Difference
|
Check
|
| 7 |
49 |
2 |
20 |
69 |
49 - 20 =
29 |
x |
| 6 |
42 |
2 |
20 |
62 |
42 - 20 =
22 |
x |
| 5 |
35 |
3 |
30 |
65 |
35 - 30 =
5 |
✓ |
To know the number of packets of long candles and short candles, we list the multiplies of 7 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 5 more long candles.
We also check if the total number of candles must be less than 70.
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
Multiples of 10: 10, 20, 30, 40, 50, 60, 70
Number of packets of long candles = 5
Cost of long candles
= 5 x 4.50
= $22.50
Cost of short candles
= 3 x 3.10
= $9.30
Total amount that Diana spent on the candles
= 22.50 + 9.30
= $31.80
Answer(s): (a) $10.70; (b) $31.80
