Wesley and Justin collected some buttons. If Wesley gave Justin 66 buttons, both would have an equal number of buttons. If Justin gave Wesley 39 buttons, Wesley would have 6 times as many buttons as Justin. Find the number of buttons each of them had.
- Wesley?
- Justin?
| Case 1 |
Case 2 |
| Wesley |
Justin |
Wesley |
Justin |
| 7 u + 66 |
7 u - 66 |
12 u - 39 |
2 u + 39 |
| - 66 |
+ 66 |
+ 39 |
- 39 |
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 Justin had at first is the same in both cases.
7 u - 66 = 2 u + 39
7 u - 2 u = 66 + 39
5 u = 105
1 u = 105 ÷ 5 = 21
Number of buttons that Wesley had
= 7 u + 66
= 7 x 21 + 66
= 213
(b)
Number of buttons that Justin had
= 7 u - 66
= 7 x 21 - 66
= 81
Answer(s): (a) 213; (b) 81
