Brandon and Valen collected some pens. If Brandon gave Valen 64 pens, both would have an equal number of pens. If Valen gave Brandon 42 pens, Brandon would have 5 times as many pens as Valen. Find the number of pens each of them had.
- Brandon?
- Valen?
| Case 1 |
Case 2 |
| Brandon |
Valen |
Brandon |
Valen |
| 3 u + 64 |
3 u - 64 |
5 u - 42 |
1 u + 42 |
| - 64 |
+ 64 |
+ 42 |
- 42 |
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 pens the same. LCM of 2 and 6 is 6.
The number of pens that Valen had at first is the same in both cases.
3 u - 64 = 1 u + 42
3 u - 1 u = 64 + 42
2 u = 106
1 u = 106 ÷ 2 = 53
Number of pens that Brandon had
= 3 u + 64
= 3 x 53 + 64
= 223
(b)
Number of pens that Valen had
= 3 u - 64
= 3 x 53 - 64
= 95
Answer(s): (a) 223; (b) 95
