Mark and Carl collected some buttons. If Mark gave Carl 69 buttons, both would have an equal number of buttons. If Carl gave Mark 45 buttons, Mark would have 5 times as many buttons as Carl. Find the number of buttons each of them had.
- Mark?
- Carl?
| Case 1 |
Case 2 |
| Mark |
Carl |
Mark |
Carl |
| 3 u + 69 |
3 u - 69 |
5 u - 45 |
1 u + 45 |
| - 69 |
+ 69 |
+ 45 |
- 45 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of buttons the same. LCM of 2 and 6 is 6.
The number of buttons that Carl had at first is the same in both cases.
3 u - 69 = 1 u + 45
3 u - 1 u = 69 + 45
2 u = 114
1 u = 114 ÷ 2 = 57
Number of buttons that Mark had
= 3 u + 69
= 3 x 57 + 69
= 240
(b)
Number of buttons that Carl had
= 3 u - 69
= 3 x 57 - 69
= 102
Answer(s): (a) 240; (b) 102
