Peter and Fred collected some buttons. If Peter gave Fred 53 buttons, both would have an equal number of buttons. If Fred gave Peter 34 buttons, Peter would have 4 times as many buttons as Fred. Find the number of buttons each of them had.
- Peter?
- Fred?
| Case 1 |
Case 2 |
| Peter |
Fred |
Peter |
Fred |
| 5 u + 53 |
5 u - 53 |
8 u - 34 |
2 u + 34 |
| - 53 |
+ 53 |
+ 34 |
- 34 |
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 Fred had at first is the same in both cases.
5 u - 53 = 2 u + 34
5 u - 2 u = 53 + 34
3 u = 87
1 u = 87 ÷ 3 = 29
Number of buttons that Peter had
= 5 u + 53
= 5 x 29 + 53
= 198
(b)
Number of buttons that Fred had
= 5 u - 53
= 5 x 29 - 53
= 92
Answer(s): (a) 198; (b) 92
