Daniel and Neave collected some stickers. If Daniel gave Neave 54 stickers, both would have an equal number of stickers. If Neave gave Daniel 30 stickers, Daniel would have 4 times as many stickers as Neave. Find the number of stickers each of them had.
- Daniel?
- Neave?
| Case 1 |
Case 2 |
| Daniel |
Neave |
Daniel |
Neave |
| 5 u + 54 |
5 u - 54 |
8 u - 30 |
2 u + 30 |
| - 54 |
+ 54 |
+ 30 |
- 30 |
1x5 =
5 u |
1x5 =
5 u |
4x2 =
8 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of stickers the same. LCM of 2 and 5 is 10.
The number of stickers that Neave had at first is the same in both cases.
5 u - 54 = 2 u + 30
5 u - 2 u = 54 + 30
3 u = 84
1 u = 84 ÷ 3 = 28
Number of stickers that Daniel had
= 5 u + 54
= 5 x 28 + 54
= 194
(b)
Number of stickers that Neave had
= 5 u - 54
= 5 x 28 - 54
= 86
Answer(s): (a) 194; (b) 86
