Perry and Ryan collected some buttons. If Perry gave Ryan 55 buttons, both would have an equal number of buttons. If Ryan gave Perry 45 buttons, Perry would have 6 times as many buttons as Ryan. Find the number of buttons each of them had.
- Perry?
- Ryan?
| Case 1 |
Case 2 |
| Perry |
Ryan |
Perry |
Ryan |
| 7 u + 55 |
7 u - 55 |
12 u - 45 |
2 u + 45 |
| - 55 |
+ 55 |
+ 45 |
- 45 |
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 Ryan had at first is the same in both cases.
7 u - 55 = 2 u + 45
7 u - 2 u = 55 + 45
5 u = 100
1 u = 100 ÷ 5 = 20
Number of buttons that Perry had
= 7 u + 55
= 7 x 20 + 55
= 195
(b)
Number of buttons that Ryan had
= 7 u - 55
= 7 x 20 - 55
= 85
Answer(s): (a) 195; (b) 85
