Luke and Paul collected some buttons. If Luke gave Paul 59 buttons, both would have an equal number of buttons. If Paul gave Luke 31 buttons, Luke would have 6 times as many buttons as Paul. Find the number of buttons each of them had.
- Luke?
- Paul?
| Case 1 |
Case 2 |
| Luke |
Paul |
Luke |
Paul |
| 7 u + 59 |
7 u - 59 |
12 u - 31 |
2 u + 31 |
| - 59 |
+ 59 |
+ 31 |
- 31 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 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 7 is 14.
The number of buttons that Paul had at first is the same in both cases.
7 u - 59 = 2 u + 31
7 u - 2 u = 59 + 31
5 u = 90
1 u = 90 ÷ 5 = 18
Number of buttons that Luke had
= 7 u + 59
= 7 x 18 + 59
= 185
(b)
Number of buttons that Paul had
= 7 u - 59
= 7 x 18 - 59
= 67
Answer(s): (a) 185; (b) 67
