Mark and Ken collected some buttons. If Mark gave Ken 64 buttons, both would have an equal number of buttons. If Ken gave Mark 38 buttons, Mark would have 4 times as many buttons as Ken. Find the number of buttons each of them had.
- Mark?
- Ken?
Case 1 |
Case 2 |
Mark |
Ken |
Mark |
Ken |
5 u + 64 |
5 u - 64 |
8 u - 38 |
2 u + 38 |
- 64 |
+ 64 |
+ 38 |
- 38 |
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 buttons the same. LCM of 2 and 5 is 10.
The number of buttons that Ken had at first is the same in both cases.
5 u - 64 = 2 u + 38
5 u - 2 u = 64 + 38
3 u = 102
1 u = 102 ÷ 3 = 34
Number of buttons that Mark had
= 5 u + 64
= 5 x 34 + 64
= 234
(b)
Number of buttons that Ken had
= 5 u - 64
= 5 x 34 - 64
= 106
Answer(s): (a) 234; (b) 106